The Treaty of Limburg, forming the European Union from the various predecessor groups.
The Adami Premiership (1994-1997, won 1994)
The Adami Premiership is notable for being the first to be headed by someone from outside Great Britain. Seen as a compromise candidate originally during Kinnock's Premiership, his views were seen as nationalist, conservative but also pro-European. This set of views simultaneously represented both wings of the Conservative Party as well as neither of them, and would quickly prove to be a problem when burdened with government.
Much of what Adami is remembered for, however, is the response to the volcanic eruption on Montserrat in 1994. Royal Navy ships assisted in the evacuation of Plymouth, and the wider island, following the eruption which quickly made much of the island uninhabitable. Many Montserratians left the island for other islands in the West Indies, but the sheer amount of Montserratians due to the virtually complete evacuation overwhelmed most of the small Caribbean islands. Most Montserratians therefore left for Great Britain, where ex-pat communities established themselves in London and several other GB cities. The UK Government provided financial assistance to many of the local governments taking in Montserratians, to expedite integration given they were de facto internal/domestic refugees. The island remains under populated, historically speaking, as many former residents are yet to return given the widespread destruction.
He did provide several smaller steps towards the growing devolved, and quasi-federal United Kingdom however, attempting to govern in the interest of the whole UK. Although accepted as a "white man" (*1) by the voting population in Britain, he was Maltese first and foremost, and worked to further federalise the UK. British Law began to specify a minimum set of nine bank holidays (public holidays) for the year, including New Years Day, Good Friday, Easter Monday, First Monday in May (Labour Day), Whit Monday, Emancipation Day, Trafalgar Day, Christmas Day and Boxing Day - although the devolved Home Nations could add extra if they desired. The legislation also provided for Northern Ireland to have extra bank holidays as St Patricks Day and the Battle of the Boyne to avoid the devolved government having to legislate on a divisive cultural topic. Scotland added the 2nd January as well as St Andrews Day, Malta added several days including Victory Day, whilst the West Indies would celebrate Carnival/Crop-over at the start of August.
Following some unease at introducing a "black holiday" (in celebrating Emancipation Day, despite the first Monday of August already being a bank holiday in Great Britain and was therefore de facto a rebranding exercise), was a significant matter which would bring matters to a head; the agreement of accession for several east European nation to the European community, despite fears over the large number of countries. A committed Europhile, Adami agreed to nine countries acceding to the European Community, and this was followed by the agreement to the Treaty of Limburg which formed the European Union out of the European Economic Community and some other institutions, as well as formalising the process towards further monetary union for many of the now-EU states. Despite Adami gaining an opt-out from the unified currency, disquiet in the Conservative Party began to rise quickly, and a backbencher rebellion began to be openly talked about. Putting down a marker, Adami brought forward a leadership election for the Conservative Party under the slogan "Put up or shut up", believing he had the majority of the party behind him, only to be proved ever so slightly wrong with a large number of abstainers, and therefore stepped down as Prime Minister.
The Major Premiership (1997-2007, won 1998, 2002)
Major was another compromise candidate during the election period, put forward by ministers who were unwilling to stomach the prospect of a further right-wing Tory candidate as Prime Minister. Major promised there would be no further significant "Europeanisation" of the United Kingdom, explicitly promising to remain out of the Schengen Agreement and Euro currency, although made it clear it was in the UK interest to continue streamlining the European Single Market for the UK's export market and increasingly important financial markets. Defeating Iain Duncan Smith in the final round of voting, John Major became the next UK Prime Minister, replacing Adami. Major was apparently a safer bet then Adami; he was socially liberal, economically conservative and a realist in Europe, seeking the trading arrangements without the European federalism. It was during Major's Premiership that the United Kingdom began being seen as the "wrecking ball of Europe" for it's ability to object to any step towards greater integration, moves which would see the "Enhanced Integration" proposal to allow members to integrate further where a Union-wide consensus does not exist (*2). Despite his image in Europe, his actions allowed him to reinforce his credentials as the leader of the Conservative Party.
By the start of Major's time in Downing Street, there were far fewer dependencies left then ever before; Antarctic Territory, Bermuda, Cayman Islands, Diego Garcia, Jersey, Guernsey, Isle of Mann, Pitcairn Islands, and the base in Cyprus (Akrotiri). A simmering territorial dispute with Mauritius meant discussions over the future of the Indian Ocean dependency; the existence of a UK base in the British Seychelles meant that it was realistically only a US base despite assertions otherwise. The United States, able to smell the wind, had begun to move operations to the Harold Holt base in Australia, and also permissions to use the British Assumption Island base in the Seychelles as well as agreements with the United Arab Emirates (the former British Trucial States). The moves allowed Major to declare that UK defence interests no longer required the use of Indian Ocean territory and allow the return of the Chagos Islands in 2016 when the lease with the United States expired, and free up a diplomatic burden for the United Kingdom. Most of the other dependencies were areas with few residents (if any in some cases); as such independence was hardly viable when the population was counted in the dozens.
Internal discussions and debate continued in the Crown Dependencies (Jersey, Guernsey, Isle of Mann) as to whether to seek UK integration or not. Although ruled over by the British Crown (and despite being treated as a British Dependency, they were constitutionally different from the other Overseas Dependencies), they continued to be largely self governing, although proposals to grant the islanders full UK citizenship had been resisted by overseas MPs (*3); "why should they get the benefits of citizenship for free, when we had to integrate to get it?", which was a difficult point to refute. The islanders continued to hold British Dependency Citizenship, giving visa-free travel to the UK for an extended period along with some simplified visa processes for employment in the United Kingdom - a status which also meant that, lacking full UK citizenship, they were not EU citizens with freedom of movement to other European countries either. It was this lack of movement stemming from their nationality rights which drove much of the debate, although the impact of full UK integration, and thus European integration with all it's effects - predominately on trade - were also a significant point of debate, given Jersey & Guernsey's geography (far closer to France then the UK).
As the dependencies withered, driven by a Government focussed on reducing costs and balancing the economy by integration or independence (or "integration or jettison" as some put it) - notably Hong Kong handed back to the People's Republic of China in 1997, overseas military action brought some back to the table. Following on from a successful deployment to East Timor under the mandate of the United Nations (together with Australia, New Zealand in particular) and action in the Kosovo War (based predominately out of Malta), Major authorised British Forces to intervene in Sierra Leone. Having learnt lessons from Northern Ireland about the need for a "good image" (in Northern Ireland seeing the use of the predominately Catholic Maltese regiments in Irish nationalist areas), the British Army made good use of regiments from the West Indies, backed up by the rest of the British Army to re-establish order in Sierra Leone whilst searching for Britons in captivity. The operation quickly expanded, and ended up de facto winning the civil war for the Sierra Leone government, forcing the opposition to capitulate. Withdrawal was not fast however, as the UK came to agreement to continue to base a British Army force of several hundred soldiers for several years, as part of a UN-sponsored peacekeeping deal, to make sure the country did not backslide in to violence once more. The intervention in the Sierra Leone civil war was one of the first major actions for the West Indies Regiments, which had normally been focussed solely on the Caribbean region, and whose history had been largely the put down of the Grenadan insurrection. The moves made the UK extremely popular in Sierra Leone, with some locals advocating for integration - a move which was quickly dismissed by the UK Government given the large Sierra Leonese population and extremely poor economy, but did see a lasting role for the UK in Sierra Leone, helping to administer an economic recovery of sorts as well as the resumption of elections and democratic government. Later actions by the British military involved action in Afghanistan alongside the United States in ousting the Taliban, but playing a far smaller and "supporting" role alongside the United States.
Domestically, towards the start of Major's time in power, the cause of university education tuition fees was paramount. The rapidly increasing numbers of students attending university was both a cause for celebration, but also a financial blackhole. Reform of the financial model for higher education quickly spun out in to a reform of the wider system of devolution funding, as education was a mostly devolved topic to the Home Nations. The end result would see the most of the taxes controlled by either Westminster (ie. Corporation Tax, VAT), or the Home Nations within certain limits (ie. Income Tax), and all proceeds split between either going to Westminster to fund de facto "federal" projects (*4), going to the Home Nations to fund devolved expenditure (or in to a separate budget for England and Wales for Westminster to spend on their behalf), and a small amount used for automatic transfers between the Home Nations for the richer to subsidise the poorer. The end result of this, for university education, was a move towards a UK-wide subsidy from Westminster per student, to finance part of their education, with the rest payable by the devolved administration who could bill the student in the form of tuition fees if they wished. The UK subsidy was greater for STEMM subjects (Science, Technology, Engineering, Maths, Medicine), and lower for others, but also rose for disadvantaged children.
Coupled to this, was the Major & Conservative led reform of the economy, as many state-owned companies were privatised. British Telecommunications was finally privatised, given the increasing competition from mostly unified cable company NTL as well as private operators such as Cable & Wireless. Much of the electricity and gas networks were privatised, whilst subsidies to British coal mines were finally abolished causing most to cease operations except where crucially twinned with a coal-fire power station. Reform of the water industry, however, remained elusive. Royal Mail took a similar approach, being broadly speaking "federalised"; the Royal Mail itself looked after inter-regional and international mail movements, whilst individual Royal Mail subsidiaries existed in each Home Nation for the purposes of local delivery & collection, and could therefore be accountable to the local administration as well. Reform of British Rail occurred along similar lines, with much of it broken up in to separate subsidiaries based around Scotland, Wales, and several large English regions. The reform of local government saw the two-tier structures abolished in favour of new unitary authorities in order to "streamline" government and reduce perceived wastage, a model rapidly copied in Wales too (*5). Similar moves had already occurred in the other Home Nations, where Scotland had abolished it's twin-tier system, and the other Home Nations had never had such layers. In years later however, the drawbacks of such a localised unitary approach became visible, as frequently the lack of cross-border co-operation hindered oversight of topics on a wider scale such as public transport or strategic planning.
Notes:
(*1) Sadly, in the 1990s I can't see a person of colour managing to lead a major political party to power.
(*2) As the UK has joined later (1980s), it's therefore allowed the initial 6 to integrate further without interruptions before the first enlargement, so I think the UK will still be trying to avoid further steps towards European integration over economics.
(*3) I know the Jersey/Guernsey/Manx have full UK citizenship in OTL; the 1948 nationality law act explicitly defined the Channel Islands & Manx as part of the colonies and not the United Kingdom in the 1948 law about citizenship (unless I and Wikipedia editors have fundamentally misread it!). By the time the next significant evolution of nationality law comes around, I can see Maltese and other overseas MPs objecting to a change in status; "why should they get UK citizenship for free when this was denied to us until we integrated in to the UK fully with all the obligations which come with it?".
(*4) Wasn't sure what to call these "federal" topics, as "national" is a bit awkward given that the Home Nations are, well, nations in some contexts. This is roughly comparative to OTL with regards to Scotland; some tax collection in Scotland goes directly to the Scottish Govt, whilst VAT revenue in Scotland is split 50-50 between Holyrood and Westminster. This also quasi-removes the Macmillan Method, given expenditure by Westminster in England/Eng&Wal on non-"federal" topics will come out of a England/Eng&Wal account rather than the UK account.
(*5) Wales still without a devolved system, given the OTL level of disapproval with it from the Welsh (see the original referendum for starters), as well as Kinnock (a Welshman) being dismissive of Welsh devolution (and indeed Welsh culture).
Probably 1 or 2 chapters, then finito. Obviously from an EU point of view, there's one less member (Malta), and they are using the UK Pound and not part of Schengen, so significant changes for Malta over OTL now.