London Fire Brigade said flames had engulfed a third floor flat and then spread to the roof of the four-storey building.
A spokesman said one person was treated for smoke inhalation.
Labour MP Rushanara Ali, who was at the scene, told MailOnline: "There are police officers and fire service personnel dealing with it - there's still smoke.
"I've been here for the last 45 minutes or so and they're just trying to take control of the situation.
"It's settling down and it seems like they've got a handle on it."
It comes as officials safety test cladding in buildings across the country amid fears that the material allowed the Grenfell blaze to spread quickly through the 24 floors.
Hundreds of families were last night evacuated from tower blocks in the Chalcots Estate in Camden amid safety concerns.
Ms Ali continued: "People are very concerned - I've spent most of the day visiting residents around my constituency particularly where there are concerns about cladding.
"There is a real anxiety about whether their housing stock is secure which I know people will be feeling around the city and country.
"This building today is not a high rise and we don't want to get into speculating on the cause but there is a general mood of anxiety - why is this happening, how are these fires happening?
"We expect regulation to work and in Grenfell tower's case they can see that it hasn't.
"People are being incredibly calm, this is a community that is very resilient so they will support each other - there are lots of strong connections and neighbourliness around here.
"But you can't get away from fact people are very anxious and upset at scenes that they've seen in recent weeks following the Grenfell fire.
"It's really important for MPs to be here, we have the local ward councillor here working closely with officers of housing associations and the council so it's really important people need to be able to ask questions."
A spokesman from the London Fire Brigade said: "Ten fire engines and 72 firefighters and officers are tackling a flat fire on Turin St in Bethnal Green.
"The whole of a flat on the third floor and roof is also alight.
"The Brigade's 999 control took nearly 50 calls.
"A man was suffering from smoke inhalation and has been taken to hospital by London Ambulance Service crews."