The fire broke out shortly before 1am on Wednesday at Grenfell Tower in Latimer Road near Notting Hill.
The tower is at least 24 storeys high and contains 120 apartments.
Neither police, ambulance nor the fire brigade have given specifics about injuries, but multiple eyewitness accounts have spoken of people being trapped inside the building.
Saint Clement Church and Saint James Church, a parish covering Notting Dale, Notting Hill, North Kensington, and Holland Park, is receiving people who have been evacuated from their homes.
Sadiq Khan, the mayor of London, has confirmed that he is in close contact with emergency services.
— Adrián Genesir (@AGenesir) June 14, 2017
According to information from the authorities, the building is expected to collapse.
There are still information about people trapped inside.