As many times I have seen the infamous Tower Bridge which is often mistaken for the London Bridge (Fergie from the Black Eyed Peas has this in her video, 'London Bridge'.) This is very interesting for people that like engineering and architecture.
When the Tower Bridge was designed, the only other way over the Thames was the London Bridge.It has Portland Stone to hide the Steel structure and was one of the most sophisticated at its time.
There you can also go see the Engine Rooms which were used to open the bridge to allow tall ships to get through.
You can combine a a ticket for this attraction with one with The Monument or you can use the 2 for 1 voucher if you take the train to London.
If you are planning to spend the day in London, I recommend visiting The Monument, Tower Bridge and the Tower of London.