Local media carried reports that some of them were trapped on the roof of the building as 40 fire engines and 200 firefighters tackled the blaze.
The London Fire Brigade said two people received treatment for smoke inhalation whilst city police said that a number of people were being treated for various injuries.
Specialist medical teams were also called into to deal with fire related injuries.
Police have set up a wide cordon around Grenfell Tower, which was built in 1974, as they fear it could collapse. (Euronews)