I can see that to move the capital would be difficult but I can also see that to move some Government Departments would be doable and have definite benefits for the people currently working in them.
My neighbours were moved years ago from London to Sheffield ( Manpower Services and Midland Bank I think) and though at the time they were all horrified they are now very thankful, having improved their life style hugely. Much cheaper and better housing, cheaper expenses, more access to the countryside etc etc. They all love it.
So, perhaps the Home Office could go to Leeds, the Treasury to Norwich etc.? It would relieve the pressure on London too.