It is cheap to travel by train, if you plan and book well in advance. The prices are variable and are similar to how air companies set their prices.
Bed and Breakfast outside London is often good value for money (about SEK 400-500). Breakfasts are often a “full English”, which is a bit like what Swede’s may call brunch.
Admission is free to most of London’s large museums, but not many people know that this is true of most of the UK.
Visit the castle ruins or cliff railway at Aberystwyth, go to the theatre in Bristol, see the university and enjoy the gardens in Cambridge, take the train to Skye, take a hike in the hills and stop off in Glenfinnan with the famous viaduct from the Harry Potter films, do some vintage shopping in Manchester’s Northern Quarter or go surfing in Scarborough.