Licensing authorities are responsible for issuing club gaming permits. There are two different types of permit available, to find out which one you need, read: Gambling Commission, club gaming permits
You will need to apply to the licensing authority where the permit will be used. This is usually the local council, if you do not know who that is, see: Gov.UK, find your local council
In West Suffolk, there are two licensing authorities, Forest Heath District Council and St Edmundsbury Borough Council. To apply, you will need to download the correct form and send it to the licensing authority relevant to you.
Gambling Commission website, licensing authorities - download the 'application for club gaming permit or club machine permit.'