12 is absolutely fine for a boy to start in MT training. Girls outnumber boys by at least 15 to 1 and the pressure put on boys to be more masculine (eye roll) at secondary means few carry on through.
NYT/BTA/school productions is a very sensible path at this age for a hobby interest now with the potential to step up later if he decides it is his life calling. 12 is the old end of child roles in professional MT so unless the child was really pushing for it and school teachers or similar had commented that he also had a brilliant singing voice, I wouldn’t go down that route.
In practical terms for dance, he needs the ‘technical’ classes, like ballet, tap, and/or modern from what you say. It’s great that he has good pick up for routines - that is something some spend years improving, so it’s a gift to do that naturally. Technical classes will help him develop the ‘right’ ways to do those steps he picks up.
Grade 1 classes tend to be an average age of 7, so not quite as young as you might think. They can join at 6, but not everyone starts then so a big enough school will have students of a wider age group. Where my DS trains, they would likely put him straight into Grade 2 or possibly 3 and evaluate after a month or so to see if it is too easy or too hard and move him if appropriate. It will always depend on the kids in any particular setting, but a new 12 year old in grade 2 or 3 would be totally normal in our set up. Some would move up quickly and some would stay there and do the full grade.
I would let him do a few weeks of group lessons, check that he loves it as much as he hoped, and then investigate the option of private lessons. They are spendy (a pound a minute is pretty normal here, but I’m in London so other places may be less) but the progress rate is huge. That would allow for the catching up you’re looking for, and he could quickly find himself in class with his peers.
The wider MT picture includes singing and acting training too. You may find a local place that offers an option that combines the three - there are more of these programmes in London but they do exist across the country. But he’s right to look for extras in cleaning up the dance. Across the week, my DS is in class for dance way more than singing and acting, but it’s a case of more concentrated teaching, as most weeks he has an acting and a singing session in private lessons while all the different styles of dance are in group sessions. Acting and singing can be done in group classes too, but just keep it on your radar as parts that all come down to dance are very few and far between.
All the best of luck to him.