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.
200 firefighters have been tackling the blaze with 40 engines.
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.
Police are evacuating Barandon Walk and Tesserton Walk adjacent to the tower, with residents asked to gather their belongings and go to a nearby church about 20 minutes ago.
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.
London Fire Brigade say there is no known cause at the moment for the blaze.
#Fire in West #London. Helicopter circling above #GrenfellTower #GrenfellFire https://t.co/D5Tpixi6dM
— 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.
There had been complains on behalf of the residents for the poor security measures and conditions of the building to the company that manages the building.
According to the information so far, there was insufficient number emergency exits in case of a fire.
There are videos where people can be seen trying to escape.
There is also at least one resident who claimed that there were people who were not allowing the residents to evacuate the building.