London needs to be turned into a new fifth home nation, also remaining as the UK capital, as Greater London practically has become its own country as it has grown & changed so much so it doesn't really represent the rest of England like New York City doesn't for the rest of the US.
I am not sure about a huge sprawling city like Birmingham, Manchester, Sheffield, Nottingham etc as the new English capital. It could grow much larger and forming its own identity like London has already repeating this problem.
I feel a older & smaller town/city such as Stratford upon Avon, Warwick, Lichfield, Shrewsbury, Worcester, Hereford etc may be more suitable for the new English capital as these are more English in character also would be attractive for tourism, nicer for spending a weekend than somewhere like an urban concrete jungle like York/Bath over Leeds/Swindon.