If it's a fairly big organisation, I would have thought that an HR department existed, of which one of their roles would be referencing.
In todays markets, references tend to only be a record of when and where an employee worked, and should not contain anyhting further than that. - not even of the department they worked in, and certainly nothing on how well they performed.
If a company were to keep any information further to that on file, it would be subject to the DPA, and it would not be permissible to pass this information on, without specific and explicit permission of the (ex-)employee.
Obviously, if company A were to be phoned by company B for a chat, that's a different matter - but there are still laws against defamation and slander.
Every contract I sign with a company will have a clause in it requiring that company to provide a reference at the end of my contract with them.