Good to hear you are OK ... sounds like a big impact and remember some injuries can take a while to show up (bruising / soreness / whiplash etc.) so don't tell the other insurance you are fully OK just yet.
My advise would be to keep a written record of all the details, witnesses contact details etc.
Have you got legal protection cover with Admiral ? If not there are 3rd party companies that could deal with the claim if Admiral don't.
Because it is clear cut that the other chap is to blame, you can claim back all reasonable costs that you incur whilst waiting for a payout / new car. Keep a record of any time off work etc. dealing with the claim. Whoever deals with your claim against the 3rd party should be able to sort out a hire car (like for like in size etc) very quickly, and get it delivered to your address.
Because the 3rd parties insurance will be paying for your car hire and all other associated expenses, they will probably try and sort the claim out fairly quickly if it is clear cut. Make sure you also tell your GAP insurers and read the small print, as they may want to handle/negotiate the value of the payout for your car (to make sure they are'nt paying over the odds for the GAP)
Hope all goes well

How old was your car by the way ? as you may come out of this £££'s up with the GAP insurance
