It didn't make our list, but Tower Bridge is certainly among the London tourist attractions that don't suck. A normal tour costs just £8 and offers truly impressive views of the river as well as a decent amount of bridgey stuff to look at.
From January, the spantastic attraction goes one better with weekly tours of the parts you can't normally see. Visitors on a special Engineering ticket will be able to visit the bridge control room, the bascule chambers (the cavities housing the bridge counterweights), and the hydraulic engine room that hoists the Bridge.
The tours will operate every Saturday in January from the 7th, and every Saturday in March. Tickets are £30, which includes an hour and a half of pontine exploration in the company of an experienced bridge guide. Book soon, though, as they can only fit 12 people onto each tour.
See also: We took a look round the 'secret bits' of Tower Bridge, including the rooftops, which are not part of next year's tours.