Eight fire engines and around 60 firefighters were called to the blaze in a flat above a shop in Bath Road.
Half of a flat on the first and second floor above a shop was destroyed by fire but no injuries were reported.
The cause of the fire is under investigation.
A London Fire Brigade spokesperson said: “This incident is a timely reminder of just how important it is to have working smoke alarms in your home.
“Smoke alarms give the earliest possible warning when a fire starts. We encourage everyone to have smoke alarms fitted in every room where a fire could start, plus a heat alarm in the kitchen. It’s important to test them regularly.
“Firefighters recommend that you have a look at our online Home Fire Safety Checker to make sure there are no hidden hazards in your home.
“The online tool will ask you a series of questions that will help us work out the level of risk in your home, or the home of someone you care for. It only takes a few minutes to get tailored advice to keep yourself and loved ones safe from fire.”
