London on $50, $180 or $700 a day

British Museum (free - the Rosetta Stone, the Elgin Marbles, the Lewis Chessmen. Allow 3 hours minimum). Walk south to the Thames via Covent Garden (free street performers).

South Bank walk from Waterloo Bridge to Tower Bridge (free). Tate Modern (free permanent collection - the Turbine Hall installation alone justifies the visit). Borough Market for a £5-8 lunch (Monmouth Coffee, raclette stands, bread).

Tower of London from the outside at night (free - the floodlit towers are extraordinary). Dinner at a Shoreditch curry house on Brick Lane (£10-14 for a full meal). Beigel Bake at midnight: a salt beef beigel for £4.

Hyde Park and Kensington Gardens (free - 630 acres of central London parkland). The Serpentine Gallery (free). Walk to Notting Hill: Portobello Road for browsing (don't buy antiques without knowing prices).

Brick Lane: the Sunday Market (if Sunday) or the Spitalfields Market. Old Truman Brewery galleries (free). Walk south to the City: St Paul's exterior, the Millennium Bridge, the Sky Garden (free with booking at skygarden.london).

Camden for the evening: the Roundhouse for a gig (£15-25) or just the market pubs. The Hawley Arms or the Lock Tavern for a pint (£6). Dinner at a Camden Market stall (£8-12).

DLR to Greenwich (£2.80). National Maritime Museum (free). Royal Observatory - stand on the Prime Meridian in the courtyard (free). Greenwich Park hill for the London skyline view.

Greenwich Market for lunch (£6-10). Thames Clipper back to Westminster (£7). National Gallery (free - Van Gogh's Sunflowers, the Arnolfini Portrait, Turner's Fighting Temeraire). Walk Trafalgar Square.

Sunset from Waterloo Bridge (the best free view in central London: St Paul's to the east, the Houses of Parliament to the west). Dinner at a Waterloo pub: pie and a pint for £14. Last Tube home.

Tower of London (£33.60 - the Crown Jewels, the ravens, the Beefeaters, 900 years of history). Tower Bridge exhibition (£12.30) - the glass walkways above the river are vertigo-inducing.

Lunch at Borough Market (£15-20 at a proper stall). Tate Modern (free) then walk the South Bank to the National Theatre. The BFI Southbank for a film or exhibition.

Dinner in Shoreditch: Brat (wood-fired, excellent, £45-60) or the Clove Club (modern British tasting menu, £85 - book weeks ahead). Cocktails at the Nightjar or the Experimental Cocktail Club.

Victoria and Albert Museum (free - the greatest decorative arts museum in the world; the Cast Courts, the Islamic collection, the Fashion Gallery). Then the Natural History Museum next door (free - the diplodocus skeleton).

Lunch in Chelsea or South Kensington (£20-25). Saatchi Gallery (free - often the most interesting contemporary art show in London). Walk the King's Road.

Dinner in Notting Hill: The Ledbury (book months ahead, exceptional modern British, £70-90) or a more casual dinner on Westbourne Grove (£30-40 at any of the good Italian and modern British options).

Train to Bath (1.5h, £20-30 return) or Cambridge (50min, £25 return). Bath: the Roman Baths (£24), the Royal Crescent, Sally Lunn's bun. Cambridge: the Backs (free), King's College Chapel (£10), punting on the Cam (£20).

Lunch in Bath or Cambridge (£15-20). Return to London by late afternoon.

Final dinner in Covent Garden or the West End: an Ivy Market Grill pre-theatre dinner (£35-45) and a West End show (£30-80 depending on seat - TKTS booth in Leicester Square sells same-day discounted tickets). The best value in London entertainment.

Private Buckingham Palace tour during the summer opening (August-September only, £30 - the State Rooms are extraordinary). Or: a private art history tour of the National Gallery with a Courtauld Institute scholar.

Lunch at The Ritz (Afternoon Tea, £78 - book 3 months ahead. The Palm Court is one of the most beautiful rooms in Britain). Shopping in Mayfair: Burlington Arcade, New Bond Street, Mount Street.

Dinner at The Clove Club (modern British, 2 Michelin stars) or Core by Clare Smyth (2 Michelin stars - the finest modern British restaurant in London, £150pp for the tasting menu). Nightcap at the American Bar in the Savoy - one of the world's great cocktail institutions.

Christie's or Sotheby's private viewing (free to attend during pre-sale exhibitions - the art on display is extraordinary and the rooms are magnificent). Then the Courtauld Gallery (£14 - Manet's A Bar at the Folies-Bergère, Van Gogh's Self-Portrait with Bandaged Ear).

Lunch at Scott's in Mayfair (the best seafood restaurant in London, £60-80). Private Bond Street shopping: Cartier, Graff, Asprey. Or a Savile Row bespoke consultation at Anderson & Sheppard or Huntsman.

Dinner at Sketch (the Lecture Room, 2 Michelin stars - one of the most theatrical dining experiences in London) or at Alain Ducasse at The Dorchester (3 Michelin stars). Cocktails at Annabel's members bar if with a member.

Chauffeured day to the Cotswolds: Bourton-on-the-Water, Burford, and a private lunch at a Cotswolds country house hotel (Le Manoir aux Quat'Saisons in Great Milton - 2 Michelin stars, Raymond Blanc's flagship). Book the lunch menu (£180pp).

Return to London via Oxford (15-minute stop at the Bodleian Library and Christ Church meadow). Arrive by 5pm.

Farewell dinner at Restaurant Gordon Ramsay in Chelsea (3 Michelin stars, the most consistent fine dining room in London, £175 tasting menu). Or The Ledbury for a more relaxed but equally brilliant £120pp experience. Thames sunset walk after.