I'd personally recommend Brazilian JiuJitsu. This sport changed my life. Over the years it's helped me lose weight, gain confidence, make friends, get fit and learn a real world skill set.

Gracie Barra Newcastle is headed by Dave Elliot who is a very good coach and competitor. I don't know much about the Dungeon guys but I've seen them at comps and their guys always do very well.

Gracie Barra Newcastle

The Dungeon

If you'd rather do a striking art than a grappling one then you can't beat Muay Thai or western Boxing.

Hope this helps.