When crews arrived at Badminton Gardens in Beaufort Road, the occupants had gathered in their common room and no one was hurt.
Two firefighters wearing breathing apparatus entered the flat to extinguish the blaze and used a ventilation fan to clear the smoke.
It’s thought a toaster caught fire and the occupant used a wet tea towel to try to put it out.
An Avon Fire & Rescue Service spokesman said: “We would like to remind people to take care when using electrical items. Water and electricity do not mix and water should never be used to put out a fire involving electrical equipment.
“If you do have a fire, don’t try to tackle it yourself. Get out, stay out and call 999.”