01 Tower of London
Tickets from €22, and the only London landmark where arriving at opening genuinely changes the visit: the Crown Jewels walkway is a moving belt, and by eleven you see them over shoulders. The Yeoman Warder tours are included in the ticket and are the reason the site rates as well as it does, so build the morning around one rather than treating it as a bonus.
02 London Eye
From €18, and the fast-track upgrade is worth it only in school holidays. The rotation takes half an hour whatever you pay, and the view is better at dusk than at noon because you get the city lit and the sky still blue. Combined river-cruise tickets are usually cheaper than buying the two separately.
03 St Paul's Cathedral
Admission from €29, which buys the dome climb as well as the floor. Five hundred steps to the Golden Gallery, and the Whispering Gallery a third of the way up is the part people remember. Closed to sightseers on Sundays, when it is a working church.