There is an indoor one in Dudley, but it's a tight circuit, and an endurance race is like 40 laps, which is tough on back and neck muscles, I was truly knackered afterwoods, I tell ya.
There's obviously Birmingham Wheels park next to the ring road, and there's an outdoor track in Coventry I've been to, which isn't bad, they offer racing in three heats IIRC, so top racers go into the final.
Outdoor is absolutely fine in this weather, so long as it's dry. They tend to be bigger tracks outdoors, with longer straights, so you actually go quicker, which I prefer.