I think it's the National B type licence you'll be needing for that. In circuit racing I think you still need to have a yellow plate on the back with a black X on it to denote you're a novice but I'm not sure about Rally Cross. The plate is to warn anyone coming up behind to overtake that you might be a bit (lot?) unpredictable.
If you have a go at the circuits then you (used to anyway) get a number of paddock passes which you can use to encourage some useful friends to come along. You'll need a trailer to carry the race car on. A motor home is also very useful in order to a) pull the trailer, b) make the sausage/bacon/sausage&bacon /sausage and egg/bacon and egg/sausage bacon and egg sarnies * in. Oh and don't forget a kettle, coffee and tea, c) a fridge to keep the milk and food as well as (in the words of Clarkson) refreshing beverages, d) to hang an awning from in order to shelter from the inevitable rain while you replace the clutch 15 minutes before the warm up lap and e) somewhere to entertain the bevvy of attractive, scantily clad young women who will doubtless flock to offer themselves up to the god of motor racing..............actually that last one might be more of a personal fantasy than a realistic probability, but, what the hell, feel free to use any of my middle aged fantasies you like.
Ah, but not that one.
* Delete as applicable.