You are right, judder00. Under the Data Protection Act, you are entitled to a copy of the information a company holds about you. It's called a subject access request.
Check out the Information Commissioner's website at
http://www.ico.gov.uk/Home/what_we_cover/data_ protection/your_rights/how_to_access_informati on.aspx for more information.
It sounds like they're trying to scare you into paying up. If you don't pay, they would have to take you to court, which would naturally involve issuing papers by post. I can only assume they don't have any records to back up their claim, which is why they can't send you any now.
As they have refused your request, you should be able to complain to the Information Commissioner, but I doubt you will get very far, and they can't give you any advice about the alleged debt itself.
However, your local Citizens' Advice Bureau will be able to help - they will review the case and help you complain to Trading Standards or the Office of Fair Trading if they agree that this company's actions constitute harrassment.