As said before, use the BGA website to look for clubs and think about when you can fly when deciding which one(s) to visit. Don't look at the distance, look at the travel time and if it's likely to be affected on busy holiday weekends. Some clubs have good facilities to stay overnight which can reduce the travelling if you are flying on two (or more) consecutive days.
Don't just turn up, ring, find out when a good time to turn up to have a look round is.
Bicester (Windrushers) is a good club, so is Husbands Bosworth which is just south of Leicester.