The usual drill is:
1. The contracted medical company write to your GP requesting info, usually within 7-10 days of the triage call. This cannot be accelerated unfortunately.
2. The GP will most often submit an invoice for payment before providing the data. Typically it takes 2-3 weeks to send the invoice, because, as stated by
@Chelonian, it is not a primary healthcare issue and therefore not a priority for the NHS.
4. The service can then take 2-4 weeks to cough-up. This cannot be accelerated unfortunately, even if you call your AFCO as it is processed by the Civil Service in a top secret bunker, not far from Andover.
5. The GP surgery can then take another 2 or 3 weeks to produce the goods, after which it's...
- A possible further delay whilst more detailed info is requested or...
- A yes/no decision is made regarding medical sutability - if OK, a face to face medical apointment is booked (typically in about 2-4 weeks). If not OK a medical rejection letter is sent.
- The only bits that can be accelerated, in realistic terms are the bits undertaken by the GP surgery but remember, it is not a medical emergency, so manners, good humour and possibly Chocolate Hob Nobs maketh the Marine.