Its as simple as that-think of a chain of events, POD etc for the English capital city to become unequivocably York, not London. Go as far back as you want-to Roman times if you like. IMO this doesn't mean London would cease to be the economic capital (its geographical position is clear in any TL). But politically-it neednt have always been so
I've got a simple one with a Cold War POD: A somewhat limited nuclear war erupts over an earlier Cuban crisis in September, 1962. The U.K. loses London, Sheffield, Manchester, Belfast, Norwich, Portsmouth, and a few parts of the Midlands(the town of Dudley is never heard from again, and Birmingham itself is rather....well, ruined), on top of some of the more important military bases.
York, however, survives, as does a few other places like Londonderry and Liverpool. And it's York that PM McMillan chooses as his home base now that 10 Downing Street is just a pile of radioactive rubble like much of the rest of London, due to it's being amongst the least immediately damaged areas in the U.K.