Each day owns one part of the city, and the order matters more than the hours you spend in each stop.
Day 1: Westminster and the Royal Quarter
Big Ben, the Houses of Parliament and Westminster Abbey sit within a few hundred meters of each other, so this day starts here and stays on foot. From Parliament Square you walk up Whitehall past 10 Downing Street and the Mounted Horse Guards, cut through St James's Park, and finish at Buckingham Palace.

The Changing of the Guard pulls the biggest crowd of the day, so if you want a view of the ceremony rather than the backs of other visitors, claim a spot at the rail before the ceremony starts. Westminster Abbey is the stop to slow down for, and Trafalgar Square is the other sensible start point if you would rather join a walking tour and let a guide carry the history.
Rain does not cancel this day. St James's Park is the part that suffers, so on a wet morning, shorten the Abbey visit and keep the walk short.
Day 2: The British Museum and St Paul's
Give the British Museum a full morning. It is the kind of collection that swallows three hours before you notice, and autumn is when museums roll out their new exhibitions, so check what is showing before you fix the day.

St Paul's Cathedral sits a short ride east and closes the afternoon nicely. On a wet day those two buildings fill the whole day between them, and on a bright one the walk back along the river is worth the extra hour.
Watch the pace on this one. Both stops are indoors, and both ask you to stand and read, so do not stack a long evening on top of them if you are travelling with kids or older parents.
Day 3: The Tower of London and the River
Start at the Tower of London, the castle on the north bank of the River Thames that has served as a palace, an armoury, a treasury and a prison, and where the crown jewels are still on show. Tower Bridge comes next, and the riverside path between the two is the stretch of London that photographs best.

For the afternoon, cross the river and keep walking. The South Bank puts the water on one side and the city skyline on the other, and the riverside walk carries you through both.
If you have to cut something from the day, cut the river walk rather than the Tower. The castle is what people remember afterwards, and the path will still be there tomorrow.
Day 4: One Day Out of the City
Save a day for the loop everyone asks about. Stonehenge is the piece that still puzzles historians, and Windsor Castle, Bath and the Cotswold villages sit along the same run of road, which is why they work as one trip rather than three.

That day tour starts and finishes in London, runs from $224 per person, and takes in UNESCO World Heritage sites along the route, so nobody in the group has to drive.
Do you need the coach? Not if you would rather keep the day for the city. The trade is straightforward: you give up one London day and gain three places you would otherwise never reach without a car.
Day 5: Loose Ends and Neighbourhoods
Day 5 is the flex day, and it fills fast. The London Eye on the South Bank gives you a panoramic view over the river, and The View from The Shard is the other high point, a viewing platform with a full 360-degree sweep of the rooftops.

Harry Potter fans should hand this day to the Warner Brothers Studio Tour instead, walking through Diagon Alley, Dumbledore's office and the Gryffindor common room, past props such as Harry's Nimbus 2000 and Hagrid's motorcycle.
If that sounds like too much queuing, stay in the neighbourhoods. Notting Hill and Hampstead feel more local than the centre, Greenwich Park is the summer picnic spot, and Madame Tussauds covers a wet afternoon if you have kids with you.