We fly into London from Milan on August 5th and out to US on August 6th, (Heathrow) giving us just short of 24 hours. Would love suggestions for an inexpensive (Hah!) place to stay and not-to-miss activities/sights. We are not the museum type.
The Arran House Hotel, www.arranhotel-london.com, is a B&B in Bloomsbury. In addition to regular private rooms (not cheap), it has dorm-style rooms at hostel-like prices. Everyone gets the full English breakfast.
Do you like the theatre? Check out what's playing at www.officiallondontheatre.co.uk.
If it's a clear day and you'd like a panoramic view, take a ride on the London Eye: www.londoneye.com.
Drop into a pub for some "pub grub" and a pint.
Do you like to walk? In London there is a new world around nearly every corner. Go exploring.
The Isis hotels near the airport are actually quite inexpensive and handy to Heathrow.
Hop on Hop off Bus Tour would allow you to cover some ground. I did the Big Bus Tour, best to get on the Red Tour with the live commentary. It also included a cruise on the Thames (1/2 hour). My favorite spots include Big Ben, Trafalgar Square, Tour of London, and I agree the London Eye would be great but the line can take a while. If you are at all spiritual try to go to an evensong service at Westminster Abbey or St Pauls Cathedral. So much to do, so little time. Have FUN!
You don't have to be spiritual to enjoy Evensong. If you just enjoy beautiful music you will enjoy it. If you stay out in Windsor, St. George Chapel in Windsor Castle has a beautiful Evensong.