You can get the information you want under freedom of information if the data protection act allows it, so in effect, your remedy is within the DPA not the FOIA.
You have no right to obtain sensitive personal data, but Section 2 of the DPA 1998 defines 'sensitive personal data' , and it does not appear to prevent disclosure of the information you require unless it is likely to cause the data subject 'distress' or 'damage' (Section 10).
So in my opinion, you can get what you want.
If this is an employer/employee relationship then another remedy is within employment/contract law. If a material requirement of the job to have particular qualifications, then I would argue that there is an implied obligation on the employee to show proof of those qualifications. Failure to provide proof would give rise to disciplinary action. Make sure you follow the correct disciplinary procedures to avoid a wrongful dismissal action.