Ask them for proof - all the relevant documents etc and check your bank statements from then to see if they tally (you can order back copies from your bank - may be a fee though).
I had a similar problem and got a free credit check from Experian. Turned out a gym I had belonged to still had me registered as a member although I had left and they claimed I had defaulted on the payments. They had passed my details to another credit company to recover the debt, but when I got in touch and insisted my membership had run out (from the year long agreement I originally signed) they dropped the claim. It left a minor default dint on my credit rating but it's not caused me any problems (been able to get credit cards and a mortgage since then).
If in doubt, get advice from Citizens Advice Bureau.
Good luck!