I think many schools are moving away from really starting GCSEs in year 9. There used to be several in this area, and now I know of only one that does. So it may be less of a problem than you think.
Also, sometimes 'starting GCSEs' in Year 9 isn't very different from what schools who don't start then do - it can mean just choosing options and giving some subjects up, and spending a bit more time on the chosen ones. But the actual work being done in maths, science, English etc is often quite similar, as they are learning skills that will be needed, or introductory facts to eg. chemistry, which would have to be learned at that stage of learning, whether it's called GCSE or not. Other subjects might start a bit more on the content, so that could take more catching up, and of course if they are already in the timetable and classes for GCSE, it could restrict the choices of someone coming in. But on the whole, starting in Year 10 around here wouldn't be a disaster, even in those schools that do include Year 9 as a GCSE year. Other areas might be different.
Not all schools set much for Year 7-9. And they might be able to get an idea from his previous work and reports as to what sets they think would be suitable - he could still move up or down in the first few weeks as they get to know him. Maths and science would be the bigger challenge - even if he's not in the right set to start with, it would be better if they knew whether he was likeliy to be heading for Foundation or Higher tiers, as those do start to teach quite different content. But even then, Year 10 isn't impossible to move from one to the other, especially if he's willing to work to catch-up in things that he has the ability, but might have studied different content.
You don't need to apply in the next few weeks in you are looking a in-year admission for Year 9 for next September. The end-Oct deadline is for those applying to start secondary school. You could move back and apply towards the end of this academic year for a place in Year 9 at the start of next academic year. I think you'd have to have moved back by then though. And that would also be the case for mid-year admission. If you're joining a school at a non-standard entry point, it's a similar process whenever you join it - start of school year or another time. it will just come down to which school has any places available in his year group. But you could start looking at schools now and then closer to the time find out which of the schools you like have places. Obviously start of school year probably makes life easier for him, and perhaps there would be more likely to be places available, given that other people also might be moving over the summer etc. Admissions-wise, though, it doesn't make a difference whether it's Sept or April, for an in-year admission. This is for standard state schools in England, starting in Year 7.
A private school would have a totally different admissions process, and you'd have to talk to them separately. They might allow him to go out-of-year, as well, if that's something you wanted, depending how the school systems fit together from where you are now, and here.
Sounds like you should start looking at schools and talking to them about the process, whether state or private, when they start GCSE, how they set, how many choices etc. It's quite possible to come mid Year -9 for the purposes of getting him settled and the school getting to know them.