I agree there are ample opportunities to stretch children sideways, particularly at primary level (whilst they are probably more open to parent input and suggestions)
E.g. our local silver prize band offers free tuition, music and instruments (Cornet, Tenor Horn, Baritone, Euphonium, Trombone, Bass, Percussion) to children of all ages and abilities.
There is a netball club at a local sports centre - cost £2 for 1.5 hours good coaching and playing (this has really helped DD to improve her sport, even though she's at a school where sport is done regularly)
There are a number of hockey clubs which are quite reasonably priced. They are mostly populated by private school children who are introduced to the sport at school but they are a great opportunity to get ahead in the sport early
We also have judo - £2.50 for 1.5 hours.
And a dance school which charges by the lesson not the term and carries forward if you miss one and yet still has a very high standard (run by someone who grew up in a very poor area and still wants to ensure dance & theatrecraft is accessible to as many people as possible).
I would advise anyone who is wavering on whether they can really afford private ed 3-18 to skip primary, use some of the money for extra-curricular and save the rest towards senior fees.
JMO!