I just googled no pets allowed hotels uk and No pets holiday cottages and Pet free/self catering holiday cottages came up if you scroll down a wee bit..over 5,000 options came up ?
I just had a look and yes, No Pets Holiday Cottages is an actual company - which is great to know! Not pets allowed hotels doesn’t seem to link to the major booking sites though to allow you to search across their listings in that way and in fact on Trivago the search term changes automatically to ‘pet friendly hotels’!