I thought it would be useful to have a thread on dog-friendly places. The first I'd like to nominate is Utter Waffle, across the road from Brockwell Park Lido. https://www.utterwaffle.co.uk/
They have a wall of fame with pictures of the dogs who have visited.
The food is fantastic too. The restaurant is new, and they are still finding their way so service isn't rapid but the ambiance is good so it's easy enough to bear with them.