When DD was at an Independent school we couldn't afford the extras and now she is at grammar we don't have the time. You can't win can you.
It very much depends on whether you are working and will be accompanying or not. The options are very different. Some of DDs friends have been on PGL adventure holidays, tennis coaching courses, singing / drama.
When we were home educating DD we did a lot of London Walks http://www.walks.com
Museums, Dockyards, Greenwich observatory etc. If this had been on offer http://www.thehacklab.uk/courses/octobe ... f-term.htm
we would probably have done something like that.
Best of luck