There are all sorts of covetable, vintage gifts at London Peculiar - and their map of London peculiars makes a lovely stocking-filler.
Amelia Parker has jewelry for men and women made with antique clay pipes. It's an amazing way to share something unique, centuries old, yet very usable. You can purchase the jewelry online, or at various markets throughout December.
For a present that lasts all year, museum membership is perfect. IanVisits has an excellent summary of what's on offer - from major institutions like the Science Museum to small and quirky options such as Carshalton Water Tower. Alternatively, cover all historical bases with membership of London Historians, with a monthly newsletter and events ranging from pub meetings to walks and tours.
Finally, this weekend is Gifted in Deptford: over 200 artists and designers are offering their work. Mulled wine and mince pies are also available, all well away from the unbearable crowds in the West End.