I am a teacher and my holidays are generally the same each year so I always remember the weather.
I can say with some certainty that May and June have been good camping weather for the last 3/4 years while July and August have been pants...until I go back to work and then early September has again been lovely!
I am in full agreement with mrneillees. I'm a Teaching Assistant and from June until we break up for the summer hols is always lovely weather.... then until we go back in Sept it remains total PANTS!!
I am not a teacher, but our June trips have always been better weather than the August ones, but it's pot luck, just go for it and make the most of the good weather on the days you have it!
My birthday is mid May and usually is lovely weather. That said a few years ago my parents borrowed our tent for a week (over my birthday) and had a cold (down to 3 deg) and wet week. My hubbie's birthday is mid June and he generally good weather but not the last 2 years. I would say consider the Norfolk if you don't know where you want to go. We've only lived here 2.5yrs, previously lived in Leeds and it's sooo much drier here, on average about the 3rd of the annual rainfall compared with Leeds! That said it is still Britain so no guarrantees...
I have to agree with the others. As someone that doesn't need to go during the school holidays, I've found that June and (early/mid) September of the last few years have been much better than August and to a certain extent July.