I haven't got my "Survivor's Guide to the UK" with me so there might be a reason why my suggestion doesn't work, or there might be a problem in your timeline I can't remember.
I would suggest Winchester, it's on the M3 and less than 20 miles from Southampton and the Isle of White. The old city is surrounded by good farmland, has a University and plenty of educational establishments as well as several high status places to house parliament (I'd suggest the Guildhall) and the Royal Family. It also has teh historical cachet of being Alfred the Great's Wessex and the old capital of England.
What better symbolic place to lead the rise from the ashes?
It's maybe a bit east for the capital.
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