London in December help.

If you’ve been here 9 times already but haven’t been further north than Warwick, or anywhere in Wales or Scotland, or anywhere in East Anglia, how about spreading your wings a bit? There’s a host of places that will amaze you out there.

But do make sure that you allocate a day to Greenwich as well, which is close to the top of places to visit in London for me.

We have enjoyed December in London twice. Your wife will find lots of Christmas decorations to enjoy everywhere. The shops and streets are beautiful with Christmas decorations and lights. We enjoyed a day in Richmond, exploring and walking along the Thames plus lunch at a local pub; if you decide to go to Richmond, consider getting tickets to Kew Gardens for their Christmas themed gardens. They become available in the summer. It was an easy Tube ride for us from central London. We also very much enjoyed a Christmas concert at Royal Albert Hall.

Christmas carol service at St Martin’s-in-the-Field church? Again, check their website as you’ll need to book in advance. If you’re into classical music, check the Wigmore Hall, Barbican, St John’s Smith Square and Festival Hall websites too.

Christmas at Kew is an amazing experience, but you will need to purchase tickets soon. This is very much celebrating like a local, and the lights simply can’t be described. They are amazing.
https://www.kew.org/kew-gardens/whats-on/christmas

For walks, start browsing the website of the London Walks Company.
They have walks in different neighborhoods in London and walks with themes such as Dickens, the Beatles, and more.
They do day trips to Cambridge and to Oxford; escorted; your guide goes with you, of course.
https://www.walks.com/

See the column on the left on this page, "The Walks", which lists them by day.
There are different walks on each day of the week.
https://www.walks.com/walks-by-day/monday/

For afternoon tea, here are 15 options:
https://www.walks.com/blog/affordable-afternoon-tea-london/
Many of the museums offer an afternoon tea in their restaurant or cafe.
Many of the finer hotels offer afternoon tea.

As for Christmas Markets, many cities and towns around the UK will have them. Bath, York, Manchester, Birmingham, Stratford-Upon-Avon, have them. It may be fun to take a day trip from London to check out one of these. If you go to York, you may want to spend 2 or 3 nights there, as there's a lot to see besides the Christmas stalls. Birmingham has a German Christmas market, with vendors from Germany selling ornaments, food, drink, and more.
(The Christmas markets in these places begin in November and run through the first or second week of December. Most do not continue on up to Christmas Eve. (But some do!) Do check out the dates online for any town you will be going to, to make sure the Christmas market will still be going on when you want to be there.)
Check out the list here:
https://www.visitbritain.com/en/things-to-do/christmas-markets-britain
https://www.thebfcm.co.uk/birminghams-frankfurt-christmas-market/

In London, here's the website for the Hyde Park Winter Wonderland:
https://hydeparkwinterwonderland.com/

Book tickets for Christmas at Kew Gardens ASAP. Very popular. There are also lovely lights at The Wetland Center.

See if there are Santa Runs. Basically charity runs. Fun to watch.

See if a traditional Christmas panto is being performed and get tickets.

Check websites for Cadogan Hall and Wigmore Hall for classical music offerings.

There’s a Christmas Market along the Thames.

Believe the Trafalgar Square Christmas Tree will be set up on Dec 5th.

As far as cozy pubs; The Antelope in Belgravia, The Red Lion Parliament Street, The Adam and Eve near the Guards Museum, The Two Chairman near St Stephen’s Green, The Dove in Hammersmith, The Pineapple in the Kentish Town Neighborhood, The Holly Bush in Highgate, O’Brien’s Irish Pub in Ealing, the gorgeous art nouveau Blackfrairs pub across the road from Blackfriars station, the Pride of Spitalfields, Anchor and Hope Riverside and The Crown in Richmond.

Fancy a pint and Happy Christmas.

EDIT: visit a Pret a Manager and order a Turkey, cranberry, and stuffing sandwich.

EDIT: Buy Christmas Cards at museum gifts shops

a third vote for Christmas at Kew. We loved it