Conclusion: three full days cover the core — explore by neighbourhood, not by checklist. ① The free museums are world-class: British Museum, National Gallery, Natural History Museum and Tate Modern are all free for permanent collections (pick two wings at the British Museum, don't try to see it all). ② The Tower of London is about £34 with slow Crown Jewels queues — book timed entry a week ahead in summer. ③ Transport: tap contactless bank cards on Tube and buses (no Oyster needed); the Zone 1–2 daily cap is about £8.10. Stand right on escalators. ④ Budget £15–25 per person on attractions and £50–80 a day on food and transport. ⑤ Airports: Heathrow Express is 15 min for £25, the Piccadilly line is 50 min for under £6. ⑥ Carry two cards from different banks in case one is declined. ⑦ Book West End shows 6–8 weeks out for cheaper seats.