London in 3 days

Westminster before the tour coaches. Big Ben and Parliament are looked at from outside and cost nothing; the best angle is the middle of Westminster Bridge. Westminster Abbey is open for sightseeing Mon–Fri from 9.30 (last entry 15.30) and Saturday from 9.00 (last entry 15.00), adults €36 — if a church isn't your priority, skip it and come back for Evensong, which is free.

Through St James's Park to Buckingham Palace; from the little bridge over the lake the palace stands at one end and Horse Guards at the other. Changing the Guard is at 11 and runs about 45 minutes, but not every day — the calendar shifts monthly, so check the night before. Free, and you claim a spot half an hour ahead.

Along the Mall and through Admiralty Arch to Trafalgar Square, then into the National Gallery. Free, daily 10–18 and Fridays to 21. Two hours, not five: van Eyck, Titian, Turner, van Gogh and Cézanne are in the west and north wings, and that is a complete visit.

Lunch behind Trafalgar Square or in Soho, ten minutes on foot. Then back across Westminster Bridge to the South Bank and east along the river, past the London Eye and the National Theatre.

Borough Market under London Bridge station: Tue–Fri 10–17, Sat 9–17, Sun 10–16, closed Mondays. You come for the cooked-food stalls — a pork sandwich, soup, cheese — not for the grocery shopping.

Tate Modern in the old power station, back west along the river. Free, Sun–Thu 10–18, Fri and Sat to 21. The Turbine Hall is a reason in itself. In the evening, theatre in the West End: the TKTS booth on the south side of Leicester Square sells discounted seats for same-day shows, Mon–Sat 10.30–18, Sun 11–16.

Tower of London, first slot of the day. Adults €43, less for children, students and seniors. Head straight for the Crown Jewels — the queue in front of the cases is at its shortest just after opening. Leave the White Tower for afterwards.

Down to the water under Tower Bridge: crossing on foot at road level is free, only the glass walkway upstairs is ticketed. From there it is ten minutes to Leadenhall Market, a Victorian arcade of cast-iron columns now full of bars and shops.

Lunch in the City, which on a weekday has the most choice; at the weekend the same streets are half empty. Then One New Change, the mall opposite St Paul's: the lift to the roof terrace puts the dome right across from you — free, no ticket.

Tube to Holborn or Russell Square, then the British Museum. Free, 10–17 and Fridays to 20.30, with a free timed slot for the Friday late. The Rosetta Stone, the Parthenon sculptures, the Sutton Hoo treasure and the Assyrian reliefs — two hours, and that is a visit. The rest without a plan only wears you out.

Covent Garden, ten minutes on foot: the covered market, buskers on the lower level and Neal Street, then Seven Dials one block north.

Dinner in Soho: Berwick Street, Frith Street and the lanes around Chinatown. Every West End theatre is ten minutes away.

DLR from Bank to Cutty Sark, about 25 minutes. The trains have no driver, so sit at the front — it runs through Canary Wharf and dives under the Thames. Cutty Sark sits on the zone 2/3 boundary and is charged as the cheaper zone, so the trip stays inside the zones 1–2 daily cap.

Cutty Sark, the 1869 tea clipper mounted on glass so you walk under the hull: adults €26; without a ticket the ship is visible from outside. The National Maritime Museum is two hundred metres on and free.

Up the hill through Greenwich Park to the Royal Observatory: adults €28, 10–18, last entry at 17. Inside are the prime meridian, Harrison's sea clocks and a camera obscura. Outside the gate, by the statue of General Wolfe, you stand free with the same view over Canary Wharf.

Greenwich Market in the old town centre, under a roof: cooked-food stalls from twenty-odd kitchens. Open daily. Next door are the Old Royal Naval College and the Painted Hall.

Back by boat rather than Tube: Uber Boat calls at Cutty Sark and runs to Westminster in about 45 minutes, on a contactless card and its own fares (outside the daily cap). Ride at the stern and the city goes past from the water.

The last afternoon in the west: Hyde Park and Kensington Gardens, the Serpentine, Kensington Palace from outside. If it rains, three steps away are the V&A, the Natural History Museum and the Science Museum — all free, open to 17.45 or 18.