Four fire engines and around 25 firefighters tackled a fire at a mid-terraced shop with dwellings above on Bridge Road in Wembley.
Half of the ground floor was damaged by the fire. Five people were treated on scene by London Ambulance Service crews and taken to hospital.
The fire is being treated as accidental and is believed to have been caused by a heat source placed too close to combustible items.
A London Fire Brigade spokesperson said: "The rise in energy costs means there’s a very real risk of heating-related fires. We know that people will turn to alternative ways to keep their families warm overnight without turning on the heating, we just want to make sure that people are staying safe at the same time.
"We know that people may want to use portable heaters to heat just one room. It’s important to follow the manufacturer’s instructions and ensure these items are safety registered and in good working order. If you’re using these items around children always supervise them carefully and place heaters somewhere where they won’t be accidentally knocked over and away from anything that could catch fire."
The Brigade was called at 1554 and the incident was over for firefighters at 1758. Firefighters from Stanmore, Willesden, Park Royal and Paddington fire stations attended the scene.