I've googled like mad but can't find anything suitable for a 12/13 year old with the a great deal of higher learning potential.
Could do with finding something suitable as school are doing what they can but have actually recommended that we look into this as they feel dc would benefit tremendously from it. They've offered a place in a term-time extension program for 14/15 year olds but dc isn't comfortable socially with this as they were bullied by a couple of older kids in primary school for being put on show as a wonderchild able to do better than the older kids and they definitely prefer to keep a low profile now at secondary school to avoid a repeat of that.
We are not based in/around London so I suspect options are limited but a residential option would be do-able.
BTW we are not pushy parents, dc do all the usual stuff with their peers, as we generally favour a benign neglect style of parenting.
I have one G&T DS and one who is just good at school in general and what they really like to do in the summer break is learn about survival skills. Some campsites do it, so you can go as a family. It's much more fun than school, and it's practical skills that have to include some science, and learning lots of practical skills, as well as persistence, teamwork, etc.