Originally Posted by
stut
Just to clarify - are you leaving the airport and taking the train the same day, or are you staying overnight in London?
There's lot of ways to do it. One option is a HOHO bus tour (there's plenty to choose from). Or, if you'd rather stretch your legs, you can see plenty from the river walkway (or, indeed, from the river boats).
If you're doing a same-day trip, you'll need to leave your bags somewhere - there is a left luggage place at St Pancras station. You can then hop on a train down to London Bridge, walk along towards Tower Bridge (with the Tower opposite), then back along towards Waterloo via Borough Market, the Tate Modern, the London Eye and finally the Houses of Parliament. Over the bridge and there's Westminster Abbey. Walk along Whitehall to Trafalgar Square then hop on a 91 bus back up to St Pancras.
You could also look into walking tours -
http://www.walks.com/ has been mentioned by several posters before now.
This is an excellent itinerary, by the way. I am in London 8 or so times a year and often bring family members and turn them loose to see thing while I work. This has some great sites (Borough Market, Tate), some iconic sites (Tower Bridge, Westminster, Eye), lots of outdoor time to get sunshine (well, daylight...) and air to get over jet lag. Wonderful fist day itinerary! It seems simple but is very well done. I am also a big fan on London Walks.
One thing I would add to the itinerary the option to walk across the Millenium Bridge at the Tate Modern and take in the view of St. Pauls as well as the Thames, or at least walking half way out over the Thames before turning back to the south bank.