Hi Hasbo.
Ive just found one called"The Chase"at Stanton Park,Leigh Delamere,Chippenham.
It has 8 pitches and not far from M4.
I have not stayed there,but it may be ideal for you?
Regards,Adrian
Hasbo.
Try www.ukcampsite.co.uk and tap in the name of the above site.
There are 9 reviews on it and it sounds lovely(Going to show it to the wife and might stay there myself) lol.
Adrian