Most circuits will allow you to practice without a licence but many events in the UK require a licence issued by the Motorsport UK (formerly MSA) https://www.motorsportuk.org and most circuits belong to the Association of British Kart Clubs (ABKC) http://www.abkc.org.uk .
Both of these websites provide valuable information on how to get started in Karting. However independent kart racing, known as IKR, has grown enormously in recent years and now probably exceeds MSUK racing. It tends to be far more economical and friendly. There is no governing body for IKR as individual clubs decide how to run their events and which categories to include although there are also some travelling championships such as NKC and RetroRacer which visit several circuits during the season.
If you need to call Motorsport UK regarding your licence the direct line is 01753 765050