Four names come up in every conversation about London, and each one asks for a different chunk of your day. None of them needs a full day on its own, which is exactly why people overspend their hours here.
Tower of London and Tower Bridge
Tower of London is the landmark where the visit happens indoors rather than in a photograph. The Crown Jewels stay on exhibition inside, and the buildings around them carry the oldest royal stories in the city. Give it two to three hours, and arrive early if you can, because the crowds build from mid-morning onwards.
Then walk the few minutes to Tower Bridge. Twilight is the moment worth waiting for, when the bridge is illuminated, and the river goes dark behind it. Is an entire morning at the Tower worth it? For history people, yes. For everyone else, two hours plus the bridge is the right shape.

Westminster, Big Ben and the Abbey
Westminster is the densest half mile in London. Big Ben, the Houses of Parliament, Parliament Square, Downing Street and Westminster Abbey sit within a few minutes of each other, and the Abbey is where Prince William and Princess Kate were married. With a single afternoon left in the city, spend it here, because you can cross five names off without touching the Underground.
Walking tours often open at Trafalgar Square and then head over to Downing Street and Parliament Square, which makes a sensible first hour for a first visit. The evening version trades the politics for ghost stories and mysteries, so pick by mood.

Buckingham Palace
The palace is the official London residence of the royal family, and visits take in many of the lavish rooms and the Royal Gardens. The changing of the guard pulls the biggest crowd of the day, and the ceremony does not take place every day, so check before you build a morning around it.
Arrive early if you want to watch the ceremony rather than the backs of heads. The palace is a short walk from Trafalgar Square, which makes the two easy to pair and leaves the afternoon free for the center-west squares.

St Paul's Cathedral
St Paul's anchors the City, the old financial quarter, and it sits on the city route that loops London's center. Give the cathedral an hour or two.
What I like here is the timing as much as the dome. Once the office crowds go home, the streets around St Paul's empty out, and from there you can walk toward the river and the Tower with nobody in front of you. Two landmarks in one afternoon are very doable.