Crews from Midhurst and Petworth, along with two Surrey Fire & Rescue Service crews from Haslemere and Godalming, were called to the bathroom fire in the property just off the A283 at 2.05pm.
According to West Sussex Fire and Rescue Service, the lives of the people inside the house were potentially saved by a smoke alarm only installed that morning.
The fire service, which found smoke issuing from all of the upstairs windows and from underneath the roof tiles, said the family had a 'lucky escape'.
A spokesperson added: "One of the crews from Haslemere wearing breathing apparatus tackled the fire inside the property, which had broken out in the airing cupboard in the bathroom.
"The crew from Petworth, also wearing breathing apparatus, targeted the fire from inside the roof space to prevent it spreading further, and working together they were able to contain the fire within the room of origin."
Petworth firefighter James Witherden said the outcome of this incident could have been 'much worse' if the family had not checked their smoke alarm and 'discovered it was defective.
He added: "Remarkably this family had replaced their old smoke alarm on the landing outside the bathroom that morning, which gave them plenty of warning to get out of the property and dial 999.
“Because the smoke alarm had alerted them to the fire it meant not only that they were able to get out of the property quicker, but that we were on scene quick enough to prevent it spreading to other rooms and causing further damage.
“Although damage was limited to the room of origin, much of the property was affected by smoke. Sadly they will now need another new smoke alarm, as the new one they fitted on Wednesday was melted by the heat of the fire, having done its job and alerted them to the fire in the first place.”
Nicki Peddle, the county fire service's area manager for prevention, said this incident 'really goes to show how much of a difference' having a working smoke alarm can have.
"Fortunately, firefighters were alerted quick enough to be on scene to bring this fire under control quickly and prevent further severe damage to this family’s home," she said.
“We would urge all residents to check their smoke alarm is working once a week and to ensure that defective alarms are replaced as a matter of urgency.”
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