Hampshire Fire and Rescue Service's Urban Search and Rescue team were called to the scene to assess structural damage to the property. The house and neighbouring properties were evacuated.
A fire service spokeswoman said: "The lorry crashed into the property cutting off the staircase leaving two people trapped upstairs in the house.
Emergency: fire crews at the scene (Picture: PA)
"Firefighters used an aerial ladder platform to rescue the people from the first floor of the house."
Officer in charge Paul Coates said: "Our crews were on scene quickly and worked hard to reassure and rescue the two people who were trapped on the first floor of the property."