Crews were called to a semi-detached property on Cromwell Road shortly 9am on Sunday, January 7.
The fire started in the unit's electrical intake cupboard but the occupants were alerted to the emergency by their smoke alarms.
Watch manager Mark Woodward said the three adults present "did the right thing" by getting outside quickly and shutting the front door so as not to fuel the flames.
The house suffered extensive smoke and fire damage and the family are being supported by the British Red Cross.
Two casualties suffering from smoke inhalation were treated by paramedics at the scene
Watch manager Woodward added: "There is a safety message there to make sure all electrical installations in your home are in good working order.
"If you suspect something is faulty you need to call an electrician straightaway, and if you hear sounds or they start to smell of smoke, obviously call 999 for the fire service.
"This family did the right thing as not shutting the front door would have allowed oxygen in to fuel the fire.
"We were there for around two hours and there was quite a lot of damage to the stairwell but thankfully there were no injuries as working smoke alarms were in place."