Westminster Abbey, a walk through St James’s Park to Buckingham Palace, then the Regent Street and Oxford Street lights after dark.
Day 2
South Kensington
The Natural History Museum at opening, lunch nearby, then the V&A; end at Harrods and the Knightsbridge lights.
Day 3
The river
The Tower of London in the morning, Borough Market for lunch, then the South Bank to Tate Modern and the Winter Market.
Day 4
Bloomsbury & theatre
The British Museum, Covent Garden and a West End show in the evening.
Day 5
Winter evenings
A slow Marylebone morning, then Hyde Park Winter Wonderland or Christmas at Kew after dark.
Day 6
Day trip
Windsor for the castle or Oxford for the colleges; both are back in London by dinner.
Day 7+
Go deeper
King’s Cross and Coal Drops Yard, Shoreditch and Whitechapel, or the new London Museum at Smithfield.
Honest thought: London is big and December daylight is short. Group sights by area, start early, and keep one evening per day for lights or theatre rather than crossing the city twice.