If you have any employees you must operate Pay As You Earn (PAYE) and deduct tax from their weekly/monthly wages. Every month (or in some cases every quarter) you will pay this amount to HM Revenue & Customs (HMRC), together with the Employee and Employer National Insurance Contributions (NICs). Be sure to make your payment before the monthly deadline - the amount of time you'll need to allow will depend on how you choose to pay. You will need to submit your payroll information to HMRC online 'in real time' on or before the day when you pay your employees.
It's fairly unusual for personal trainers to have any employees, but you should contact your local HMRC office to obtain an Employers start up pack if you are planning to employ staff.