If you provide your staff with access to sporting or recreational facilities, this can be a tax free benefit in kind for the employees providing that certain conditions are met, although gym membership is unlikely to qualify.
The facilities must be available for use by all of your firm's employees and must not be available to the general public. The facilities do not have to be used exclusively by your firm's employees though, so if you jointly offer the facility with another firm and their employees use the facilities too, the membership is still tax free.
The cost of the membership is not tax free where the facilities are open to the public, or based at a private residence or holiday accomodation, or where the membership provides you with use of a vehicle (which includes boats and aircraft).
You may wish to consider securing preferential rates at your local health club or gym rather than offering to meet the full cost of the membership, as the provision of the membership will be a taxable benefit in kind and your staff will be taxed on the amount you pay on their behalf.