Sorry for necroeing an old thread but I wanted to add my recommendation for Lady Dinah's Cat Emporium. Went their yesterday. it's a lovely place, very calm and relaxing. The food is scrumptious, although it's difficult to concentrate on when you're preoccupied with the cats. (But on the subject of food, if you have the high tea you can ask for as many top-ups of food and drinks - as you want.
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We were downstairs, there are several cat trees, as well as walkways close to the ceiling, which give the kitties their own space whenever they want.
We saw three kittens (about five months old), including one little ninja boy who'd been found wandering along Shoreditch High Street when he was about 10 weeks old. He spent the whole time lying on a cushion being adored by a stream of people.
Although it was fully booked for the day, there were always a couple of tables free so it never felt too crowded.