Tony Blair emails a draft copy of A Journey over to David Miliband including the passage where he talks about the 2001 election, where he takes Bill Clinton's advice to treat an easy-win election as if every vote mattered. With this in mind, DM takes a more cautious approach to launching the Movement for Change (inspired by Blue Labour/community organising principles) as he anticipates the discomfort it may cause in existing party structures. He waits until he wins (unlike OTL) and then begins efforts. Blue Labour comprises comparatively more of the Labour Party's agenda between 2010-2015 and it encourages the party to be more aware of the loss of its base to Ukip, prompting more efforts to establish a socially conservative agenda.
Or, a more fun option: for whatever reason (maybe the Icelandic volcano in 2010 erupts longer and does more environmental/economic damage) the 2010 election leads to a Tory-Labour Grand Coalition (or a 'Big Coalition for a Big Society') in the face of an 'unprecedented economic threat' to the country, of the likes of the 1930s. Labour's Blue and Purple book factions find a surprising amount of common policy ground with the Big Society and Red Tory factions and invest more money in community organising efforts to make this model viable for local authorities. Over the rest of the parliament the Liberal Left bolsters the ranks of the Greens creating a statist-ish left, the Lib Dems attract disgusted Blairites and Tory modernisers and stake out a libertarian-ish agenda, and the political scene fractures into four parties of reasonable size. But in the next election, though the Lib Dems and Greens have picked up some seats (and Scotland has SNP'ed itself), the overall electoral calculus favours a continuation of the Big Coalition. Whether or not it continues, Labour has learned (or extirpated those who refuse to learn) the value of playing to a conservative value set and organisational structure.