How many of the class are likely to be tutored? We never considered it for either DC as they had no problem with concepts and though they were nowhere near the top of the year, were doing fine. It was only afterwards when we realised what had been going on, and that DC were probably more natural mathematicians than we had realised. The school will give strong predictions to those who are performing well, in part because they can be sure they will get the grades, but the next step, without support could be difficult for those who have been tutored. One impact, in very academic schools, is that other kids can start feeling they are not good enough. The turnaround at University for DC and several of his friends was noticeable. None made Cambridge, but did very well elsewhere.
Maths teachers, particularly those teaching A level, tend to have a reasonable idea of who is a natural.
My advice would be to apply to where he wants to go, then work really hard to nail the A star and in parallel plan for a super gap year. Internships, even a low level job in a bank found through an employment agency. Then some travel, perhaps gain a language. And keep reading. Follow some interesting economists on Twitter and read what they recommend etc. Look at the public lecture programmes for places like the LSE, many of which are now on line, and attend.
Several from DS' high achieving school took gap years and almost all seem to have done something constructive. They also applied for internships and other work experience. By the time they graduated, many had a pretty impressive Linked In profiles, and moved smoothly on to good graduate jobs. Contacts would have got them some of this, but the willingness to keep applying and to give up time and vacations to build an employment profile will have contributed.
Someone suggested that mathematicians should not take gap years. I am not convinced. Firstly Financial Maths is largely iterations of statistics so mainly new and nothing to do with ability in, say, mechanics. Secondly DD took an intercalation in Bio Medical Engineering at Imperial at the age of 22, which involved a crash summer course in maths before, effectively, being dumped into the third year of the engineering degree. Some did just fine, others struggled, the deciding factor seemingly being maths aptitude rather than age or previous grades.