Forty engines were called to the 27-storey Grenfell Tower at just after 1.15am on Wednesday, on the Lancaster West Estate, north Kensington.
Witnesses could hear screaming from the upper floors as the flames rose and one desperate resident could be seen waving a white cloth.
Police say a "number of people are being treated for a range of injuries", including smoke inhalation, as pictures from the scene showed flames shooting metres into the sky and engulfing most of the block.
The fire brigade said 40 fire engines and 200 firefighters had been called to the blaze in Grenfell Tower, which has 120 flats.
"Fire is from 2nd to top floor of 27 storey building," the fire service said on Twitter.
"Firefighters wearing breathing apparatus are working extremely hard in very difficult conditions to tackle this fire," London Fire Brigade assistant commissioner Dan Daly said.
"This is a large and very serious incident and we have deployed numerous resources and specialist appliances," he said.
London mayor Sadiq Khan tweeted: "Major incident declared at Grenfell Tower".
Actor and writer Tim Downie, who lives around 600 metres away told the Press Association he feared the block could collapse.
"It's horrendous. The whole building is engulfed in flames. It's gone. It's just a matter of time before this building collapses.
"I just hope they have got everyone out.
"People have been bringing water, clothes, anything they've got to help, out to the cordon.
"I have seen people coming out in their bedclothes - it's just very distressing."
Residents are being evacuated from the tower block, the Metropolitan Police said.
The cause of the fire is not known at this stage, London Fire Brigade said.
Fabio Bebber wrote on Twitter: "More screams for help as the fire spreads to another side of the building.
"We can see how quick the fire spreads via the external panels. It's unbearable hearing someone screaming for their lives at #grenfelltower."
George Clarke, who presents the Channel 4 TV show Amazing Spaces, told Radio 5 Live: "I'm 100 metres away and I'm absolutely covered in ash.
"It's so heartbreaking, I've seen someone flashing their torches at the top level and they obviously can't get out.
