I just had a quick google and the Dogs Trust came up. Their holiday cottage search facility goes up to the option of 3 pets, and for interest I clicked '3 pets', and some random parameters, and a lot of options seem available.
'Bakers Mill Holiday Cottages' in Dorset - we have been going there for the last 3 yrs and can again have many dogs as you like.
The cottages are small but each have individual gardens for the inhabitants dogs, and as it is on a farm, you can take the dogs straight out for walks without going off the property.
We stayed at hall dunnerdale cottages in the lake district, and if you book through them and not the agents they said we could take all 5 of our dogs if we wished! Really lovely people and beautiful location, with lovely walks straight from the front door. In the comments book they leave on the side, someone had even taken their cats with them!
Beadnell Beach House in Northumberland is great, took our four dogs there this summer, access straight onto the beach and a fenced (low fence) patio at the front useful for drying off before they come inside