The first thing I would do on your journey is take part in various rental/corporate events and see if you'd to progress in the sport.
As you gain confidence you would then progress and maybe get your own Kart and take part in test sessions at your local track and Kart club. Join their club and take part in club test days etc. Get to know some people in the pits and get chatting.
When you are ready to go racing order your license pack from Motorsport UK. This costs about £60 and included your first license fee. Study the videos they provide you and learn the flags etc.
Once you are confident you know the basics on and off the track then you can talk to your local club and book your ARKS test. There is a practical and theory part. No need to worry, it's very simple.
Complete your ARKS test and fill out your license form, which which your club will stamp. Send it off to Motorsport UK and you should then get your license.
You can now take part in various club races and events!