You can lay all the concrete and erect all the steel you like (funded in whatever way you want) but if the airlines don't want to come then the additional facilities aren't going to get used. Manchester only last year finally surpassed its best previous passenger throughput in 2006, and even now the number of aircraft movements are barely more than 2/3rds of what they were back then. Passenger and movement capacity hasn't been a limiting factor at MAN for almost ten years now. What makes people think that throwing more money at the airport will suddenly make more airlines want to use it?
If the capacity at Heathrow (or Gatwick for that matter) was upped substantially then I'd wager it would be utilised almost as quickly as it was built - if that was allowed. Up capacity at Manchester by the same sort of magnitude (however it is funded), and I bet it would take quite a lot longer before a lot of it was needed.
Cut it any way you want, but the greater demand is in the London area. Even with the current constraints down south there has only been some, but not a huge sway towards launching new routes to more northerly airports. You cannot force airlines to use Manchester rather than London - a few might take the bait, but many will say if I can't serve London I won't bother, because the yields are softer further north even if I could fill all the seats.
So if significant additional central government investment did get put into MAN, where would all the traffic come from to fill the infrastructure that was created?