A very sad, and typical tale Hugh. Did you carry your EHIC card? In the small print of most policies covering European travel there is a clause requiring you to insist on a public hospital if you are ill. Standard practice with tourists in Spain (and I suspect elsewhere) is to call a private ambulance and send you to a private hospital. They will commonly insist on some assurance that their bill will be paid. Obviously, I do not know what ailed you, but public hospitals in Spain are usually first class.
As far as getting your money back, have you asked why Allclear will not do the reimbursement, that is why you take out insurance after all? Otherwise you might as well just use your EHIC card and get free public care (ultimately funded by the NHS). I fear that you stand little chance of getting your money back from a Spanish private hospital, a route which in itself seems rather strange. Have you spoken to the Financial Ombudsman? failing that I would send a demand to the private hospital in Spain to see if they intend to settle anytime soon, if not ask for a Legal Complaints form and say you intend to take out a 'Denuncia', that might just oil the wheels. There are some no win no fee debt collectors around in Spain who might be willing to act for you.
To be honest, I don't think they are liable as the insurance company should pay you, but £2,500 to return home in good health doesn't seem to me a bad thing. I fear that if the sources I mention cannot help, then a letter to say the Daily Mail financial people may do the trick, otherwise, is it worth continuing to pursue this and probably make your health worse?
Mike.