At the Tower of London we got there before 10 (were shooting for 9 but were late), got tickets and walked right in, no line. I followed the advice on this site of where to get tickets, and we went to the Crown Jewels first, etc. I basically would each attraction to plan the details here in America before I went. Then I had a chart in Word, printed and took it with me & each day while I was there would review the details so I knew what was coming the next day. It saved lots of time over there. Google "Tower of London Rick Steves Forum" to get details on that place, then do the next one, etc. It takes some time here, but better here than there.
London Eye we went on a rainy day in May, no line. Great view. Didn't mind being soggy.
Westminister went late in day (accidentally) and maybe a 5 min. line.
Buckingham Palace was horribly crowded for the Changing of the Guards, but don't know what to do about that because even if you're early people will get there later and try to shove you out of the way.
British Museum had no wait and we went midday in May.
Stonehenge we did the early tickets, for 6:15 am. You have to fax a paper request to them but was totally worth it. We were there, all around the stones for an hour with 8 other people. Amazing.
So just research each thing and find the best strategy that will work for your trip. Maybe a Plan A & Plan B. But I'm a planner. I don't like wasting time over there because I didn't do my homework. It won't all go according to plan and that's fine, but at least you have done your research.