The London Fire Brigade states on its website that 20 fire engines and around 125 firefighters were alerted to the fire that broke out just before 4 pm local time.
Among other things, a step car with a 64 meter high ladder - according to the authority Europe's tallest - must have been mobilized.
The fire broke out on the 17th floor of a 21-storey and 79-meter-high building that houses apartments and offices.
The building was evacuated quickly and no one was injured in the fire.
The fire is not yet under control.
The cause of the fire is still unclear.