Try to go during the shoulder season when school is in or it will be very busy.
I just love the UK, but while I could go on and on about destinations there–Liverpool, Edinburgh, Bath, Cambridge–if I had to make only one recommendation outside of London it would be the Lake District. It's so beautiful and so welcoming. Try to go during the shoulder season when school is in or it will be very busy. Read: London and the Lake District: 12-Day Itinerary.