When dealing with references, the data protection and disclosure rules are slightly different to other "personal data" covered.
Firstly, you couldn't claim unfair dismissal as, unless you have two years service or the reason for the dismissal/termination of contract is discriminatory (i.e. sex, race etc) then you are not covered.
As for contacting the referee, the company/individual that issued the reference is not obliged to provide a copy as it was between them and your new employer. You will have to submit a "subject access request" to the company who received the reference and for a "reasonable fee" (it use to be limited to £10, not sure what it is now) they should provide a copy within 40 days...make sure you send the request registered post and keep a copy of the letter.
For more information and template letters, check out the Information Commissioners office website...its something like ICO.gov.uk
Hope this helps and good luck.