Hi Madmechanic
There are a few decent sites around Bridgnorth.
At the top end of the scale is
Stanmore Hall Touring Park This is a first class site with excellent reviews and is a couple of miles from Low Town, Bridgnorth.
Even closer and within walking distance of the town via the banks of the Severn is
Riverside Caravan Park
This park is mainly statics but with a few touring pitches with ehu along the riverbank. It's a pleasant five minute walk into Bridgnorth, it's dog friendly and apart from some occasional traffic noise it's fairly quiet. We've stayed here and it should fit the bill. There are several other C&CC certified sites with ehu, have a look at the
C&CC Sitefinder
If you were looking for somewhere right off the beaten track and very quiet then I'd recommend
Kites Nest Farm 01746 785009 This site is about five miles from Bridgnorth and lies about a mile up a farm track. As the name suggests the site is on a farm but it's remote, has hard standings and ehu and it's dog friendly. The farm track is a bit bumpy in places so take your time. Kites nest is around £10 per night and is another one that we've stayed at.