As much as I love cats, I not keen on pets around when people are eating and I don't like them being fed from the table. My cats are pretty good at not pestering, except when I'm preparing something they particularly like in the kitchen. They usually get a few titbits in their bowls.
I've been to the one in east London and am going again in June for a birthday tea.
The place is spotless and "patrons" are discouraged from feeding the cats because they are all rescue cats, some with special dietary requirements, and, as a result, they don't bother anyone for food.
We go to a pub in West Wittering after our beach walk where we can take the dogs in. Most of them slouch under the table, except ours, who sits looking at everyone longingly.