If you were facing having to relocate and could choose anywhere ...

[Alloverbartheshoutingnow]

Where would it be.

There are some constraints....

Needs to be close to a mainline rail station and airports

I'd probably not choose to go into London.

Bristol and the southwest is not an option as that is where I'm moving from
I'd prefer to avoid the west midlands as well.,

Liverpool. Culture, transport links, everything a big city has plus beaches and easy access to North Wales.

We live just off the top of the Cotswolds/ just below the West Midlands in Worcestershire. Direct (but slow) train to Oxford/London, 30-45 min drive to Birmingham airport (and also to the very good rail service from there)
Lovely area and v reasonable house prices as its just that bit too far to commute to Birmingham everyday, though once Worcester Parkway station opens and gets trains to Birmingham that might change

Edinburgh
Leeds
Newcastle

Leeds
York
Edinburgh

Melbourne or Brisbane

But if we're sticking to this country then Bath

Sorry just read your OP properly and not the South West. OK how about Cambridge