The lady I know from freegle has just said about the membership they offer on the Dogs Trust site. I went to sign up for it and it said to phone a certain number if there's already a direct debit set up to them. 1 minute 37 seconds later and the pup is covered.
I doubt we'll ever use it, but the £25 a year will go towards helping the dogs that are already waiting for a home and will help them to pay any other claims that other people make as well. £25 is a tiny amount to pay for the peace of mind it gives you!