Hi,
Contact them a month before your membership is due to expire (in writing and send via recorded delivery as proof of letter sent - keep a copy of the letter as well). Explain that your membership is due to end on XX date and you wish to terminate your membership with immediate effect as soon as this date is reached. Ask them to confirm (in writing) that they have received the letter and that your wishes will be carried out.
It needs to be exactly one month notice, if you fall after this you will pay the difference in dates. If your membership is due to end on 20 December, send the letter on the 16 November (accounts for delays in post and fitness first reading the letter). Send letter to head office and include your membership number, address and other pertinant information.
You should have no problem.