Re: It's this bit that worries me the most:
It'll be more like a builders estimate: "Build bathroom with all fixtures and fittings: £5k" sounds reasonable so you sign. Turns out walls, ceiling floor, sink,toilet and plumbing weren't explicitly mentioned so extra £15k needed.
The poor sod at the MOD who signed for this was probably under the illusion that all the bits were included in the contract but not having thirty years writing contracts with invisible gaping holes in didn't know. If he had known he would have been paid to move to the other side of the contract. If his contract with the MOD states he cant work for the opposition for x years he will get gardening leave in Eden to get him out of the way.
This, to a large degree, is how government IT has worked since PFI etc has been around and I doubt its any different elsewhere.