Looking for sites which offer storage in Cotswolds

We have recently moved into Wiltshire and are looking for a dog friendly caravan site within around an hour north of the M4 corridor. Having had a couple of nightmare journeys to the south coast along the A350 we have now decided we would rather travel north for our weekend retreat.

Our van is currently situated in North Devon, and we will hopefully move location once a suitable place is found. We prefer not to tour but to have the van sited in one place we can visit.

So... specifically... require a nice site with at least basic facilities which offer caravan storage at a reasonable price, will accept dogs (we have 3 very well behaved Golden Retrievers) no children (all grown).

Doesn't have to be Caravan Club site but will consider joining if a site which offers all requirements can be found. Haven't been able to find anything suitable despite online research.

Anyone willing to offer some suggestions? Thanks in advance.