I see David Cameron has been talking about Open Source again as too has Tom Watson. Shame really that "Open Source" is seen as some sort of panacea solution for Government IT. It isn't. The key is actually the development methods and strategies that are used.
It doesn't matter if the software being produced is bespoke, or if it is closed, or if it starting from a GPL based and worked upon. Although I would say that it would be rather silly for Government to use the GPL for it's more important projects. Why would you want to develop a system where you then have to tell the whole world the way it works. Kind of silly from a security point of view isn't releasing the source of your systems?
What needs to happen in Government is the embracing of Agile methodologies as opposed to the current old-fashioned waterfall methods which spend time ind esign then implementation and don't deliver tangible things on the way. Whether the code you develop is open or closed matters not a jot.