We opted not to purchase the hop on hop off bus tour. Rather, in ONE DAY, we visited the top sites using public transportation. Here's some tips.
1. There's lot to see. If pressed for time, mark all your top sites you want to see and map it out.
2. Number your top destinations, 1 being the most priority.
3. If in London for 1 day, buy 1 + 2 Zones tickets. It is cheap and will cover all your top attractions. You can use it on the bus or the Tube.
Theses places were visited using the bus route 11 from Liverpool St. via Victoria. From here it passed all the hot places: St. Paul's Cathedral, Fleet St., Trafalgar, Parliament, Downing St., near Buckingham Palace, Strand. We got off at Buckingham Palace and decided to opt for the Taxi. It was too cute not to ride one! From Buckingham, off to London Eye and Big Ben.
At Big Ben, took the Tube to the Tower of London and London Bridge. Then, took the tube all the way to Baker St. where we visited Dr. Watson and Sherlock Holmes. Of course, a trip in London wouldn't be complete if we didn't visit the Beatles Store next door.
For our stay, we used Hotel.Com. Got a really nice two bed room apartment that sleeps like 8! It was in Bayswater and close everything. Not to mention, next to Hyde Park, Kensington Palace, and Notting Hill.
Definitely need more time in London but for one day we saw 95% of everything.