If the Liberal Democrats don't form a coalition with the Tories in 2010, the most likely scenario would have been a very shaky Labour/Conservative grand coalition (David Cameron as PM, Gordon Brown as Deputy PM, and possibly with the Cabinet Ministry of his choice) that falls apart within a year.
Second most likely scenario is probably a Conservative Minority Government, but that also falls apart as soon as Cameron is able to call for a snap election.
To quote another prime minister - no, no, no. Grand coalitions aren't a thing outside of wartime in the UK, and if one did happen in those circumstances then they'd be major splits in both main parties. And Brown is probably one of the most partisanly anti-Tory figures in the Labour Party at that time.
