Smoke was seen rising from a balcony half-way up a block in Darfield Way, in the north Kensington area of London.
The tower block is just 200 metres from Grenfell Tower where a devastating blaze killed 72 residents in June 2017.
A spokesman for the local fire service said: "Eight fire engines and around 60 firefighters have been called to reports of smoke in Darfield Way in Notting Hill.
The blaze has now been brought under control.
London Fire Brigade said the blaze was under control and there were no reports of any injuries.
It said fire crews are speaking to residents in the building to reassure them.
London Ambulance Service urged people living near the scene of the blaze to keep their windows shut.
It is understood 25 people called the emergency services around 11.39am. Crews from across London are at the scene.
Samantha Findley, 41, said she smelled what she thought was burning plastic in the tower block and immediately left her 10th floor flat.
She told PA: "I smelled it. So I thought 'let me get out, I'm out'. I grabbed my keys, my phone. I'm out. I'm not seeing where it is or anything. I'm out."
She added: "I was concerned. I was very fearful."
Standing looking at the block and pointing towards Grenfell Tower which is a short walk away, she said: "That's Grenfell there as you can see. That was my first instinct when I smelled smoke. Everyone is thinking of Grenfell."
Dhin Chittenden said she cried as she ran down the steps from her 11th floor flat in Markland House.
The 26-year-old receptionist, who has lived in the building with her husband for a month, said she was already fearful about another Grenfell Tower-type tragedy before Friday's fire broke out.
She said: "I kept thinking about that. If it's happened somewhere else then it could happen again."
A maintenance worker at the tower block knocked on the couple's flat and told them to leave. Standing in her slippers, Ms Chittenden said: "I just grabbed my phone, my keys and ran downstairs."