Two appliances and crews from High Wycombe attended, along with an officer.
Firefighters used two sets of breathing apparatus, one hose reel jet, one covering jet, a thermal imaging camera and positive pressure ventilation.
The outbuilding was 100 per cent damaged by smoke and around 80 per cent damaged by fire.
Fire and smoke damage was also caused to an adjoining house.
One woman escaped through a first floor window of the house, uninjured, before they arrived.
Firefighters carried out a Fire and Wellness Visit and put up a smoke detector and a heat alarm.
The fire is believed to have started in a tumble dryer in the outbuilding.
Firefighters would like to remind people of the importance of following our kitchen appliance safety advice, as well as closing internal doors to prevent smoke spreading if a fire starts.