At 4, the classes even in London will be about having fun. As they should be. Most will be a combination of singing, dancing, and drama at that age so the typical class includes sitting in a circle and saying hello to everyone, some question and response like make the noise of your favourite animal and pretend you’re eating your favourite food, a basic fitness warm up that gets them on their feet without just running like a puppy with the zoomies indoors, some dance steps that emphasise rhythm like step touches, marches, stretch up high then touch your toes, building eventually to something that looks like every other smiley preschool dance you’ve ever seen, and singing along to a mix of nursery rhymes, Disney songs, and possibly an older standard, depending on the teacher. It’s all very fun and play based but it is all helping with life skills that can be useful whether the child goes on to be a performer or not. Learning when to be quiet and listen as well as how to speak so everyone could hear you, following directions, cooperating with other children, body awareness and healthy movement, appreciation of music. They aren’t going to work on scripts before they can read but I think mine did memorise a poem with the class at that age. That was about as fancy as it got.
Signing a four year old up for any activity is a case of thinking yep, they might have a good time, and then seeing if they do. Could be the tiniest class at a stage school or it could be Brownies or whatever else. It’s play based learning to be more confident and cooperate with others. You don’t need to go to London if you’re not already there - find somewhere close to home at this age.
If you think at all that your child will make a profit at this game, go give yourself a stern talking to. There are many long standing ‘businesses’ out there making bank by taking advantage of parents with stars in their eyes and open wallets. The performance industry is massively oversaturated. There are literally thousands of submissions for every job and everything that comes before the performance is your expense - the training, the photos, the equipment to record audition tapes at home, the travel to in-person auditions. The opportunities that pay more than a teeny tiny amount are exceptionally rare and will come down to looks and tone of voice, neither of which you can control.
Find a local class and give it a go. If your child loves it more than they have ever loved anything ever, then you buckle up and figure out how to manage the rest as she gets bigger. If she doesn’t think it’s the absolute most exciting thing in her life, let it go and appreciate her talent at home, take lots of video clips to keep for your family, and just let her have fun and gain confidence. If she later decides it’s something she wants to take seriously, that local class will be more than enough to step up to something more specific. Above everything, it is not about you.
All of the above coming from real lived experience. Have fun.