There are so many things to do in London, this is a very big challenge!
So depending on what you want to do, especially during the day:
If you want to go shopping, Harrods on Bond Street of course is the most famous place to shop. Do not miss getting “Ben’s Cookies,” at some point, they are in several popular places around London. This picture is of when I had only one day in London, went to Harrods’ Dolce & Gabbana make up store then got a bucket worth of yummy cookies!
If you want to go to museums, one of my all time favorites is here: the Victoria and Albert Museum.
Then decide on a play since it is mandatory in London to do that at night. Though England is known for not having good food, the Belgo Centraal Restaurant is certainly some of the best food! It can be found in Covent Garden.
London is one of the greatest cities on the planet but if you only had a day, there is still plenty of things to do!