The important thing is to find out the exam board, and then all the school's he could possibly go to within a radius that you're happy to have him travel.
If your employer will stump up for an educational consultant, they can do this leg work for you.
Then having identified schools where there is no obstacle to him continuing towards the same exams (with your fingers crossed about order of work so far and how he settles). You apply to all/most of them.
State schools: unless you are returning Forces/other qualifying govt staff, you cannot apply until the DC are in UK. You make one application, to your local council stating a preference (not a choice!) of 3-6 schools. They allocate one, or if none have. A space, they allocate you the nearest one with a space. If the allocation is unacceptable, then you can appeal (and I think you might have a persuasive case). But of course all this can take weeks and add uncertainty and stress just at a time you don't want more.
Handed considering private schools. If your DC is doing IGCSE then you may well find that it's only private schools which offer them across all subjects. Also, private schools will accept applications from overseas, and you could have a place sorted for him to start as soon as you're back. So there are objective reasons for for doing this (despite likely astronomical fees) at least for yrs10/11.
A consultant will be able to tell you more about what schools are like, and it's worth using the Good School Guide (though they write in a kind of code, so look at several entries to see what isn't said as well as what is). And using the search function here to see if your long- and short- list schools have been discussed before, or starting a thread to ask about them if you can't find a recent one.