How can I warm up a small north facing sitting room?

Yellow walls would warm up the room, or you could go for terracotta, or try cushions in reds, orange, yellows.

Yellow can be counter intuitive in a dark room, dependent on the shade. I have what was a small dark sitting room but the wall was knocked through, even though it is in shade most of the day still it doesn't feel cold.
I only get sun here in summer evenings. It is rare for rooms to be totally north facing- but even so I would go for a scandi look- blues, whites with splashes of red and mustard!
Warmth can be created with small texture changes with cushions, throws etc but lighting is also key. With new light bulbs you can create all sorts of warm tones.

Pale grey looks good with mustard, and keepingquiet has made some good points.

I too, would go with cushions and throws. I'd look in charity shops, cushions only need basic sewing skills.
I've posed elsewhere on similar topics, that we cover neutral walls with pictures - these are not expensive, mostly birthday cards, using frames from charity shops / car boots.

The Dulux Light & Space range works well to brighten a room.

If you have control of the area outside the window you are in luck. We had lawn and replaced it with light coloured chips. The difference was amazing.

Some good suggestions here.

I'd just like to add that we had a north facing sitting room in our first house and it was blissfully cool during hot spells, particularly the summer of 1976.
It never seemed cold in winter either; we did have a large radiator and a fire.

It depends how much light you get in too, we did get a lot as it was one storey up with a big picture window and we used light warm earthy shades.

www.farrow-ball.com/how-light-affects-colour#:~:text=North%20Facing%20Rooms,as%20possible%20around%20the%20room.

is your sofa fabric or leather? There are paints for different sofa fabrics as well as for leather so you can change you sofa colour fairly inexpensive if you wish so.
There is many sofa upcycling video's on the internet and they point you to the correct paint make - just google it.
A change in sofa colour will give you more options on what to do with the rest of the room.

I wouldn't use brilliant white on the walls or any white or colour with a blue undertone. But there are many shades of white on the market with a cream or yellow undertone which would warm the room visually and also tone in with your sofa. Then I would add a warm coloured rug on the floor and some textured cushions.

My bedroom is due north facing and I have gone for a terracotta and gold theme. I have some really thick ,double lined curtains which made it nice and warm when it’s dark and cold outside . Since changing the colour scheme from neutrals I have noticed and real difference! Good luck!!

www.google.com/amp/s/www.idealhome.co.uk/diy-and-decorating/best-white-paint-walls-172455/amp
And I suggest you buy some sample pots, paint each one on A4 sheets of paper and stick them to your walls for a couple of days. You'll soon discover which shades look best at different times of day and in different lights.

If you have control of the area outside the window you are in luck. We had lawn and replaced it with light coloured chips. The difference was amazing.

We found that too - we put a light coloured resin over the tarmac drive and the light bounces off it.

Our sitting room is north facing but we do have quite a wide window at the end, so it's not too dark in the Summer. We have wooden floors and used to have a large pale blue rug. We replaced it with a deep red one after we got flooded and I was surprised how much darker that made the room, even with light walls.

Warm colours, warm feeling fabrics will help, as will subtle lighting. Many people expect white walls to help but it rarely does as it can be a very cold colour as can yellow; some of them can be very cold. Counter intuitively, dark colours can make both dark and small rooms look bigger and warmer. Dark greens and reds can be very cosy. Have a look on pinterest, there are some very talented amateur decorators who have turned small, gloomy terraced rooms into lovely, warm and welcoming places to sit.

Thanks to everyone for your helpful suggestions - I'm going to try Dulux Transcend for the alcoves and a warm white for the other walls. I have lots of colourful cushions, in Indian shades, turmeric, orange, pink, etc. I don't want the walls to overwhelm this very small room as I have quite a lot of pictures and interesting things on display.
www.google.com/search?q=dulux+transcend&tbm=isch&ved=2ahUKEwiUvp6Bg43wAhVD0OAKHR6gAqMQ2-cCegQIABAA&oq=dulux+transcend&gs_lcp=CgNpbWcQAzICCAA6BQgAELEDOgQIABADOgYIABAIEB46BAgAEBhQrPEOWLSJD2CeoA9oAHAAeACAAYABiAGHBpIBAzYuM5gBAKABAaoBC2d3cy13aXotaW1nwAEB&sclient=img&ei=2ON-YJTyI8OggweewIqYCg&bih=582&biw=1280#imgrc=by6-5J1PaHol_M