Let's start with the basics..
Pre- New Labour, the government had actually a couple of clued up insiders that were (eventually) defining some structure, set standards and generally were imposing some sanity on the mess. You can say what you want about the CCTA, but they were actually heading in the right direction. Clued up people were the first to go under New Labour, because pork consulting projects and clued up insiders don't go together, both in IT and contract management.
The next thing was to rig the NAO so that "creative accounting" and abysmal project management would go unnoticed until such time as it was time to deliver, at which point pure politics kept the pork flowing where there should have been penalties instead (referring back to the lack of contract negotiation and management skills again).
In summary, what needs to happen is a return to good IT fundamentals. Structure that works across government, but with enough flexibility to allow local variations. When you set a doc standard like Open Documents it becomes pretty much irrelevant what OS of apps you use (why do you think Microsoft decided to game the ISO setup to the point of breaking it?).
You end up with a migration strategy which in the end gives you the convergence and thus the savings you need, and as pure side effect it may actually run better too (and you become supplier independent, also a great way to improve negotiation position. That should save enough money to re-employ the clued up and the sane at a salary that will actually be attractive and lose the dead wood to the consultancies they have been sponsoring for so long.
But hey, that is probably too revolutionary..