The article is an interesting take on what might have been - despite being written purely to reverse a referendum deal with which the author disagrees and to absolve Labour of any failings to produce a "progressive coalition" in 2010, despite Nick Clegg having said Labour had practically no negotiating strategy. He knew he could and did get a better deal with the Conservatives. Such a coalition would also have been a minority in itself, not the 361-seat coalition (35 more than the 326 needed) that Cameron and Clegg negotiated.
But suppose Labour took the initiative and the coalition survived for 4 years. With no austerity infrastructure investment remains at a high level but with a vastly depleted Treasury expect to see raised taxes (Vince Cable et al. would oppose business taxes, perhaps a land value tax or higher VAT as a compromise). Wrangling over a tuition-fee ceiling (£5,000/£6,000 rather than £9,000). Extra spending for Scotland, Wales and Northern Ireland may occur but again subject to government finances, probably at a lower level.
An altered Fixed-Term Parliament Act would certainly happen - the alt-May 2014 election would probably see a Conservative landslide after 17 years of New Labour and the Liberal Democrats suffering comparable losses to 2015, and a SNP surge dependent on the timing of the Independence Referendum. Such a referendum would still be lost, but with a sizeable minority - years of distrust against 'the Establishment', Westminster, all three parties campaigning for a 'No' vote, etc., would see a strong, but failing, 'Yes' vote.
David Miliband may very well have been the favourite to succeed Brown, but Alan Johnson has said he contemplated running in such an event, or else Harriet Harman as another continuity New Labour candidate. Expect a challenge from the left - Michael Meacher, Dianne Abbott, etc. After their 2014 loss expect Labour to lurch rapidly to the left, blaming their reliance on the Liberal Democrats as rendering them unable to enact further left-wing policies. Brown's successor would face challenges to their legitimacy, being over 40 seats behind the Conservatives and would be hammered repeatedly by the Opposition for being the largest party in the Commons.
Despite Cameron's status as a two-election leader expect him to face serious sniping for failing to unseat Brown. Either he remains leader of a party snapping at his heels - a certain verbally ambidextrous blonde-haired fellow will be one to watch - or else he will stand down; Osborne would be the continuity Cameronite, and (something this article does get right) either Fox (or Davis, he's stood the past two times), to be the challenger from the right. Again, the article is correct in that Fox would probably implode at some point over something minor.
As for foreign affairs - Miliband I can see backing airstrikes into Syria and leading the call for NATO intervention in Libya, Johnson, Harman, other Blairite/Brownites, not so much. Expect there to be some government embarrassment from TL's Chilcot Report. A more assertive response to the Russian invasion of Ukraine is likely.
One trivial point will be how this neoliberal coalition treats the funeral of Margaret Thatcher - very much her ideological inheritors (in part), despite being the opposition to her politically. A smaller-scale funeral is more likely. Don't expect to see the Queen present. And on that subject, I can see the Succession to the Crown Bill being passed as OTL, if not with a few grumblings from republican Labour backbenches (assuming the firstborn is still male - something the POD doesn't affect but that a writer of a timeline could experiment with).
Beyond the 2014 election, all bets are off. Depending on whom is leading the Conservatives, I can still see an EU Referendum being called, and either passing or failing narrowly. UKIP will be around in this timeline, a little weaker at first since they have no Conservative Establishment to rally against, but certainly making inroads in Northern working-class Labour strongholds. Euroscepticism will certainly be a consistent trend, if a little neutered. Assuming that the EU referendum passes and the then-Conservative government does not repeal this timeline's Fixed-Term Parliament Act, the 2018 election would take place in the middle of Brexit negotiations, opening up a whole can of worms. The further you move away from 2010, the more butterflies emerge, the more scope there is for interesting change.