Sort of. The ruling, as a result of a case between a gentleman named Durant and the Information Commisioner (and it's attendant appeals) is that information has to be stored 'in a relevant filing system'. A general rule of thumb is 'the temp test' - could a temporary worker be expected to locate the requested information reasonably quickly.
In short (and covering some points already made)
You have a legal right under the Data Protection Act 1998 to see any information held about you, subject to a few possible exemptions (such as info not being held in a relevant filing system).
Employment references are normally held for about six years after termination of employment, so you should expect to see them in your file. Your current employer may be obliged to removed the name of the person giving the reference (for a work reference, not a personal one).
You can expect to receive the information within 40 calendar days. If you do not, you are entitled to make a complaint to the Information Comissioner. If you are not satisfied with his decision, you may appeal to the Information Tribunal. Buenchico has already provided links to the Commissioner's website.