Xenia, re "hit a drum and sing "wheels on a bus", in DS state primary a third of the children receive individual instrumental lessons during the school day, the school has two choirs and a school band, with lots of opportunities to perform including music assemblies, fairs, and an annual concert where all children get to play solos.
Re Latin, AFAIK prep children won't start it till yr 7 which is the same time state primary educated children will start it if they go onto a secondary that offers it.
Re extracurriculars and clubs, DS school offers chess, music, art, rugby, football, tennis, cricket, netball, drama, ICT, etc and have run termly clubs on photography, the school magazine, lego building, code breaking, art, library club, etc. They also take part in debating competitions and spelling bees. Every year group put on their own play and there are numerous drama workshops happening. French is taught to all from Year 2 (one weekly class) and there is also afterschool French and Spanish clubs.
In terms of DT, yes, no good facilities for this but we were able to find carpentry and metal work workshops for DS during easter and summer holidays, and again, because I was not paying school fees, I never thought twice when it came to paying for holidays activities which were affordable. Same with swimming.
In terms of specialist teachers, I think they are more important as of 11, and I like the fact that if the teacher considers the art project they are working on requires the whole morning, he/she is able to bend the timetable and have them doing art all morning (it has happened).
So that's why I think that if you can be in the catchment of an outstanding primary, the money a prep will cost is not worth it... unless you are so rich you don't even notice it.
My views re secondary schools are quite different though!