My thoughts on a British scenario, spelled out once again. Every time I repost it gets longer - by 2020 I should have a fair-sized novel.
Somehow we set an English policy where they give the odd lordship to a colony or two in the last years of the 1600s. These American Lords are for some reason given American estates/titles, not British ones. Now at first there's no way they'll be allowed to sit in the House of Lords. Heck, the
Scottish Lords weren't allowed to sit for years after the
Act of Union. That's okay - they'll be admitted when the Scots are, probably, and in the meantime there will be less restraint at offering more such theoretical lordships.
America already had a few "first families" in each colony that tended to predominate in local politics. Offering a lordship in the family becomes a standard carrot to get the colonies in line. With the movers and shakers in the colonies competing for the privilege, the colonies are much more tractable. With some of the American Lords cooling their heels in London, trying to wiggle their way into parliament, there's also more awareness of American attitudes. One result of this is the end of deportation to America, with the colony of Georgia instead being founded in OTL Natal as a way to provide labor to a base in the India trade. Our Georgia ends up named Savannah.
By the outbreak of war in 1754 almost every American colony has at least one (unelected, hereditary) representative in the Lords. A few have as many as five. Appointment of new ones has completely stopped as part of the deal to allow them to serve, which has created a fair amount of tension in the colonies. The war sees, as in OTL, massive British successes that disrupt the balance of power. Unlike OTL, William Pitt retains power at war's end and dictates a harsh peace, keeping the Philippines, Cuba, and a couple Caribbean sugar isles above and beyond most of French North America.
The larger consequence of the war is that Britain attempts to pay for it by exacting taxes from the American colonies, who demand much more representation in return. Rather than have a House of Lords
entirely run from America, a deal is brokered. Each American colony will be reduced or elevated to having a single Lord. In exchange for the reduction, local federal government will be devolved on the (English-speaking, white, protestant) colonies. As a result, the kingdoms of America and Great Britain share both a monarch and an upper house. Georgia/Natal is folded into the same arrangement shortly after.
A war in the 1780s sees an over-confident Britain attempting to force some issue on the continent. Every power in Europe either goes to war with them or chooses varying degrees of hostile neutrality. Very little is accomplished except to bankrupt France, which proceeds to have a revolution. A series of wars to dominate/liberate Europe ensues. While the continent is a mess, the British-Americans go colony hunting. The Dutch carefully play along with the French on the continent, so the East Indies, Cape, Ceylon, and Guyana are annexed. The Spanish are forced to play along, so American forces occupy most of the Caribbean, Panama, then land at Veracuz and march to Mexico City. The Portuguese in Brazil are still friendly, and allow a coordinated effort to take Buenos Aires, which is turned over to Brazil. The Brits also pick up France's bases in Madagascar, Mauritius, and West Africa.
When France is finally driven back to hexagonal shape, Britain plays a major role and has large forces on the continent. As such she gains an enlarged Hannover out of the bargain and keeps most of the colonial spoils. With settlement of Australia begun, local governments sending Lords to London exist on three continents. Four if you count Britain as Europe.
In the ensuing peace the British colonies expand, sometimes against the will of Britain herself. Conquest of India proceeds. The center and west of North America is settled. Burma is grabbed in one gulp instead of three. Afghanistan is held onto, despite the mess. Portugal can't hold onto Brazil and Brazil can't hold onto Montevideo or Buenos Aires, so Britain eventually steps in, imposing protectorates on Uruguay and Argentina. Belgium revolts and requests British protection under a spare heir of the house of Hannover. Reforms in the European-descended empire result in provinces having the right to elect members to the House of Lords, and a seat being provided for the Kingdom of Hannover.
The Chinese are more aware of British strength when the Opium War comes. Unfortunately, this is actually a bad thing. Chinese preparations allow them to overwhelm and humiliate the limited forces that turn up from Manila and Jakarta, but are utterly useless against the strength sent to avenge them. Redcoats march to Peking, and then... why not? China is made a protectorate. In Tibet and some costal provinces local administration is gradually taken over by London.
The equivalent to OTL's 1848 occurs in 1856. Liberal revolutionaries in the German Federation offer the crown of a new state to the King of Prussia. Rejected, they offer the leadership of Germany to the King of Hannover instead.... The ensuing war pits Prussia and Austria (both struggling at home), some conservatives from the German and Italian minors, and a healthy Russia on one side against Britain and popular movements across central Europe. Britain wins. Poland, Hungary, Bohemia, Italy, and Germany gain statehood, while Austria and Prussia lose it. Alaska is annexed.
Bohemia, Germany, and Belgium are incorporated into the London-centered federal....
thing. This marks the first time a large number of non-Anglophonic "Lords" are elected. It also is the first occasion of the use of the term "World Parliament" to describe the House of Lords.
By 1875 the (voting) British Empire comprises the OTL mainland US and Canada, parts of northern Mexico and Argentina, South Africa, the Guyanas, most of the Caribbean, Namibia, Australia, New Zealand, Great Britain, Belgium, Ireland, Germany, and Bohemia. Much of former Spanish America is agitating to enter this category, as are the Philippines. If your perspective is mere control, the British Empire has the entirety of North America and Australia, most of the population of Asia, a quarter of South America formally (informally, all of it), and the whole center of Europe. Through it's own colonies and states browbeaten into helping fight the slave trade, it sets the course of events in most of coastal Africa, and is pursuing the slave trade inland.
For a hundred years, one thing leads naturally to another. In 1975 the World Parliament is a literal descriptor of the government in London, although proportional voting hasn't come to dominate.
Thoughts?