Love all these places! Edinburgh, York, Oxford, Cambridge, Bath!
Winchester Cathedral Close and water meadows area is stunning.
Wells is on my list to see!
London has to be broken down into areas / villages as it's too vast! In no particular order:
Hampstead Village - walk to the Heath stunning
Mayfair Mount street area
Primrose Hill
Nooks and crannies around Westminster / Great Peter Street
St James Park
Greenwich Naval College / riverside area
St Paul's area & view from millennium bridge
Parliament Hill
The city skyline from jubilee bridges at sunset
Richmond riverside and park
Chiswick riverside
Notting Hill pastel houses
Wapping
Little Venice
The Guildhall in the City of London
And for the person asking about more modern architecture, I recommend wandering around the Barbican complex (an incredible example of a Brutalist vision of community living) complete with the highwalk weaving in and out of high rise glass skyscrapers, the ancient Roman city wall and the church of St Giles Cripplegate, (survivor of the Blitz and site of a church for over 1000 years). It's beautiful.