Admiral is not the insurer but only acts as a broker. Looking at their website does not show a proper document including their full Terms of Business, although I found a document regarding charges in respect of car insurance, which does not mention any charge in respect of making a claim, therefore I would lodge a formal complaint if they do add a claim charge, unless this charge appears in the policy documents that were issued to you.
Admiral should check on the MID database that the other vehicle was insured, and subsequently put in a claim against the other party.
Draw a sketch of the incident while the facts are still fresh in your mind, ready to accompany your claim.
Make a claim, if the other party was not insured, Admiral and your insurers should take the matter further with the compensation bureau and the police.