Your son is quite a bright lad to have got such good results sitting exams two years younger than usual. In some ways, irrespective of the visa issue, he's in the same boat as other very bright children. If he goes into a state school, they will insist that he joins the "correct" year for his age, working toward GCSEs in spring 2026. The system is very inflexible that way. He could simply rack up a number of additional subjects which he hasn't previously studied, but I'd worry the pace will feel slow and he'd be bored there.
The plan you originally had of letting him have a break this year could work, if there's something he'd like to do during that time. He is still of "Compulsory School Age" until June 2026, but he could be home educated instead of going to school. (A previous poster mentioned being "registered as home educated", which is incorrect: there is no such thing as a register. The government is trying to change the law on that, but there's no way it would go through in time to affect your child.) Your only legal responsibility is to actually educate him. However, there is great flexibility on how to do that. He could learn something new, unrelated to his previous subjects, or explore some topics of interest in depth. Open University has some courses which may appeal. Or he could do practical life skills. He could have a part-time job, though there are restrictions on the hours he can work, as he is still under the scope of child labour laws until after CSA.
He could start sixth form or college from autumn 2025, but he will still be a year younger than the others, and you'd have to check that they would take him. In principle there's no reason they can't, but some settings are quite rigid about that. Don't let them tell you they can't claim government funding for an under-16, because that isn't true. Some colleges are unaware of how to do it, and may need to be pointed in the right direction.
After your son finishes Compulsory School Age, the legal situation changes slightly. It will no longer be YOUR legal responsibility to educate him. From then, HE becomes responsible for remaining in education or training until his 18th birthday. However, penalties for noncompliance were never introduced, so in practice he can do what he likes.
Anyway, come over to the Home Ed board on Mumsnet if you want some more ideas of options outside of school/college.