Yes there could be a delay if you need adaptions on your car.
But 7 -10 working days to actually do the repairs is the normal time frame for non structural repairs ( basically if the chassis not been bent which I very much doubt it will be)
im not sure with RSA but some insurance companies have a clause that that won’t take action if the third party is with the same insurance company.
But im sure you’d know that by now.
Yours may likely need a new bumper.
Or some new fixings or fixings repaired and then painting. Not a big Job.
Your partners will take longer if he has damaged all the panels down one side.