If you are only there one day you will not be able to see too much. It is best to try to see a few things in the one area rather than rushing all over london.
If I was taking someone to London and only had one day I would start down by the river, near Big Ben & Houses or Parliment.
Walk past Parliament and Westminster Abbey (or go in the Abbey), then up Whitehall, going past 10 Downing Street, then the Cenotaph.
Continue up Whitehall (which was the site of a HUGE palace in Henry VIIIs time) to Trafalgar Square.
Leave Trafalgar Square down Pall Mall (where the Marathon finishes) and go to Buckingham Palace.
Behind you is St James Park which is a great park to stroll around with loads of ducks and birds eating out of your hand, and a quick stroll takes you back where you started the walk.
If you did that walk it only covers a couple of miles but could take you half a day or more if you stopped and looked at some of the sights.
And by doing that walk you see the home of our Government, Church, Royal Family, pay respects to our war dead, and see a load of interesting buildings, history, and statues on the way.
I cant think of a better way to introduce yourself to London.