Yellow I considered mentioning about the Real Tennis champ!
There are also national gymnastics and chess champs at the moment, I seem to recall.
My DD doesn't do sport, although she goes to the gym with me most weekends. Her SEN condition means she is crap at most of the wide variety on offer but she has a deal with the PE staff that so long as she runs around for most of the lesson being active they don't mind if she isn't anywhere near the action (and she isn't). This was before she got injured obviously. :(
In terms of activities though - she does four instruments to a very high standard (one of which is exceedingly niche, and which she to be fair doesn't learn in school although she will be leading a group of players once she is in the 6th form). She has between 4 and 5 lessons a week, in and out of school, some of them >1 hour, and she plays her first study instrument in a national ensemble. She has additional lessons from an international level tutor on her first study instrument. Apart from the international level tutor, her music teachers all teach at the independent as well as the state schools. She does all the usual choir, jazz band, clubs, orchestra, festivals stuff too. On top of that she goes to a very well respected theatre group at weekends (well attended by kids from the local independent schools) and she certainly goes to or performs in > 20 concerts/plays a year. In the national ensemble it is true that many of the other kids/young people go to (or went to) independent schools - but by no means all of them.
DS does much much less but he could do as much if he wanted to. DD2 is only at primary but she does way more (at a younger level) mainly because she is a nutter. We will have to cut down on her performing activities when she goes to secondary school, I think. Her contemporaries in her out of school activities are again mainly, though not all, at independent school.
I have no doubt that the extra curricular activities at most independent schools are great. I object to the fallacy that kids at state schools cannot access the same level of opportunity if their parents are prepared and able to pay and facilitate it.