That would go down like a lead balloon with all politicians, how would we look to the outside world, like our leaders don't know where to go, a central London Parliament is the best option, everyone knows where they then
You can't upsticks the many who work for the government, have a look at the BBC who are relocating, though i don't know how much of the operation, to the north, and many employees are unhappy with the move.
Cost ten times as much in the longer term