If I had 4 spare days in the UK I would go to Cornwall. You can get the train from Paddington, then alight at Reading on the way back and get the RailAir bus back to LHR

I'm not a fan of the Cotswolds, far more brutally spectacular scenery if you go to York then make your way to somewhere like Robin Hood's Bay.

I also don't like Oxford, too Inspector Morsey for my tastes, and full of students and bicycles. My little cathedral town of choice is Canterbury.