Everyone at the cafe and the upper floors of the building was evacuated by the time fire service got to the scene.
The fire was now contained and firefighters were dampening down hotspots.
Six pumping appliances and three specialist appliances attended the scene.
Café manager and co-owner and manager Simon Holtham said the fire was believed to have started in an electrical socket behind a kitchen wall.
"From what I understand in the kitchen behind a wall, possibly from a faulty plug. From what the chefs say that's what they think happened.
"They heard a bang and tried to put it out but when they couldn't called the fire brigade."
He said the blaze appeared to have been brought under control quickly.
"There's a lot less smoke than there was 10-minutes ago which hopefully means they have got it under control. It looks a lot calmer now no one is running around."
It was the first fire at the well-known café, he said.
"You can see inside form here and there doesn't seem to be any damage in there I think because it's inside the walls it might have gone up a little bit.