It's a real mix and you can definitely dress up if you want to.
I went to see the Nutcracker (matinée) last Sunday. Not London but not far from London either. With my daughter and a big group (teachers, pupils and mums) from her ballet school.
There were lots of people in casual wear. Some people REALLY dressed up, especially mum and daughter pairs, in long glittery party dresses/evening dresses. There was even one lady in a ball gown. Then some people mid way between the two, wearing what you might wear to go out for dinner in a posh restaurant.
I went for the middle ground and wore a nice dress with a smart coat and smart shoes. My daughter (age 10) went casual in tracksuit bottoms and t shirt and fluffy jacket, just her preference.
Honestly, any of those options were fine, no one got pointed at or disapproved of. I loved seeing the mix. I think it's great people can go to the theatre in their comfies if they feel like it. I think it's great people can go to the theatre fully dressed up if they feel like it.
Personally I wear casual clothes a lot of the time, to WFH and run errands/taxi the kids about. I like the chance to get my nice stuff out of the wardrobe for an "occasion", in the same way i like wearing my traditional office clothes to the office even though most people don't, because it makes a nice change and it's a shame to have nicer clothes and never wear them. Fair play to the 100% casual folk who rejoice in never having to wear a suit or dress though. Anything goes these days!