Great serendipity, Boroughonian. As I was writing the post yesterday, I thought of starting another thread on exactly this topic.
I was particularly pleased because when SoBo was still SoBo, I often ate breakfast there, together with my dog. But then the new owners didn't allow dogs and that was the end of my two poached eggs and a cuppa there. The cafe on Grange Road doesn't allow dogs either.
In Bermondsey Street however. things are different: the new Ramen place, Cafe Murano, Pique Nique and the Woolpack all allow dogs. Locanda del Melo on Long Lane also welcome dogs.
When I saw pictures of Russell Tovey in the White Cube with his dog, I tried the same but wasn't allowed in. The dog had to be carried.
I don't know about Mangal and Nabattee, I still have to ask.
All coffeeshops allow dogs. The Giddy Grocer are also dog friendly.