Yes I've been there too, about 10 years ago - it looked just like a 1950s cafe, but the food was great.
There used to be a Mildred's on Cherry Orchard Road in Croydon, around 1984ish - which was just around the corner from where I lived. It was fantastic and incredibly eccentric. Ran by two elderly sisters, basically you dined in their front room, of a Victorian terrace - but the food was amazing. Even my total carnivore friends loved it.
I did wonder if it was the same people running the Soho one.