The Freedom of Information Act only applies to the actions of public bodies, such Government departments and local councils.
The act which you're referring to is the Data Protection Act. That requires anyone holding information about you (with certain exceptions) to divulge that information to you upon receipt of a written request. However the body divulging that information is entitled to charge a fee for doing so. The maximum fee is usually £10 but there's an exception relating to credit checks, where the maximum fee is just £2.
If you need more information about the FOI Act or the DP Act, this Government website will tell you everything:
http://www.ico.gov.uk/
Chris