Consult any official GCSE materials if you have them. According to AQA, which administers GCSE results, you can find this number along the top of any official GCSE materials under the heading "Candidate Number."
Call your testing center directly. AQA further states that individual centers, not the GCSE or any awarding body, allocates candidate numbers. When you speak with the representative, make sure and provide her with your full name, date of birth and any other features that may help her look up your candidate number.
Contact any schools to which you have had your results. According to AQA, institutions cannot process GCSE results without the candidate number, so if you've already sent your results off to a school, chances are good that the school has your candidate number and can provide you with it.