Japan House - Lighting Up Tokyo: Edo Hand-Painted Lanterns (3 December)
This free event will cover an expert demonstration from fourth-generation lantern painter Murata Kenichirō, with an introduction to Tokyo crafts. They're also hosting a lantern-painting workshop so you can try yourself, although it's sold out.
The Aldgate Winter Festival (6 December)
This wholesome community festival offers an evening of 'music, dance, light, and celebration' in Aldgate Square, featuring local performers, a lantern parade, community feast and more.
2 days earlier on 4th December, they're also running 2 free lantern-making workshops.
Visit Eel Pie Island (7 and 8 December)
Eel Pie Island in Twickenham is a tiny, unusual island home to artists’ studios. It’s only open to the public a few times per year.
It’s a great place to get some Christmas cards/gifts, and there's usually a small stand selling (inexpensive) mulled wine and mince pies. There are all kind of studios open selling jewellery, ceramics, paintings and more. There’s even a resident cartoonist.
Free sustainable crafts workshop at the Southbank centre (14 December)
Southbank Centre are running a free crafts afternoon with textile artist Sue Man. You'll learn how to make a drawstring bag/pouch with discarded textiles, and there's also a DIY 'make-your-own-Christmas-cracker' workshop with Elizabeth Jackson. There will also be a performance by a live choir.
Watch a preview of Season 2 of Squid Game at BFI (16 December)
Not very festive, but BFI is showing a preview of the first episode of Squid Game season 2 before it launches on Netflix after Christmas.
Science Museum Festive Late (18 December)
This is the Science Museum's first ever 'festive late'. There will be carol singing, talks on the science of festive themes (e.g. the physics behind Santa), mathematics-based decoration making workshops, mulled wine and more.
General admission is free but I'd recommend the VIP ticket if you're able to, as queues to get into the late evenings can be super long even if you've booked a free ticket
‘The Chemistry of Christmas Baking’ talk (20 December)
The Royal Institution is hosting two Christmas-themed talks this December. In this one, lasting 1 hour 15 minutes, chemist and baker Josh Smalley will explores the science behind festive baked goods, and 'why they make our food taste, look and smell delicious'. They're also hosting one on 'The chemistry of a candle'.
Watch 'A Christmas Carol-Ish' at Soho Place Theatre (throughout December)
Alongside 'A Christmas Carol' at the Old Vic, which seems to have quite good reviews, there's also 'A Christmas Carol (Ish)', which recently transferred to the West End at Soho Place theatre. It's received very positive reviews and still has affordable tickets on offer.
Curated Makers Christmas Market in Battersea
Turbine Hall B in Battersea Power Station will house stands from 20 small businesses and individual creators at a time from Friday 6th December until Sunday 22nd December, making it a good choice for handcrafted gifts (although realistically, probably fairly expensive ones given the location).
The power station itself and the surrounding area is also one of the most festively-decorated areas in London, including a massive 30 ft Christmas tree just outside and a bunch of festive food stalls.
Watch 'Love Actually' with Taste Films (multiple dates)
At £82.50, this is by far the most expensive suggestion. I haven't been myself but the reviews seem to suggest it's worth it. Taste Films offer full three-course (or more) meals that match the film you watch - which in the case of Love Actually, unsurprisingly includes a full Christmas meal.
You can see the full set menu on their website (they don't do substitutions/different options) so you can see whether its worth it for you or not.
Nice to a list with some genuinely lesser known suggestions - thank you!