Multi-country tour or just one?
#21
London doesn't have to be expensive. If you take the September tour LSE has student dorm rooms available: https://www.lsevacations.co.uk/Home.aspx - or the B&B I use is not expensive and is convenient for the Piccadilly line in from LHR: https://www.ridgemounthotel.co.uk/ There are a number of other B&Bs on the same street (a UK B&B is not a posh place like the US ones). You can eat cheaply if you want to - I recommend the sandwiches at Pret a Manger for lunch - and the best museums are free.