In my school, the Oxbridge/medic/vet/dentists internal deadline is the end of September. Staff wrote subject references in July. The 2 weeks between 30th September and 15th October is for their references to be written and checked. The internal deadline to apply to take the pre-uni tests (e.g. BMAT) within school was around 21st September.
Once those have gone off, the other students do theirs. There is a notional deadline of the end of the autumn term, but to be honest I have known kids who have suddenly decided over the Christmas holidays that they are going to apply, and it has been done before the deadline.
To the OP, I'm a bit surprised that you have not been included by the school/college in the process. However, all is not lost. Firstly, your son does not have to apply to uni for September 2019. He could get his results and then apply for a September 2020 start. He could focus solely on getting great results, then use the time after his A levels to do some research on universities. Alternatively, do some research now. Although open days are interesting, you can learn a lot just by visiting the university at a weekend/half-term. Even though I'm a native of the city (albeit in SW exile!) my DDs hated my home city university. It's RG, has an excellent reputation, the city is amazing (they love shopping there when we visit relatives) but they just thought it was too big and impersonal. Both much prefer smaller cities or campuses. By visiting the universities, they whittled their long lists down.
Finally, don't panic about the chat on here about how many offers people have received so soon. The vast majority of students will not have yet put their applications in, so please do not worry.