Orphaned during the Dalek invasion of Earth in the 22nd century, Barbara was adopted by David and Susan after the human victory. She was named after Barbara Wright, an early companion of Susan's grandfather, the First Doctor.
On one occasion, while her parents were getting supplies, Barbara met the Seventh Doctor, to whom she briefly spoke, but quickly departed. She never discovered his true identity. (PROSE: A Time & a Place)
Despite being adopted, Campbell looked very much like her mother. (PROSE: Legacy of the Daleks) This was true to the point that the Seventh Doctor mistook her for Susan upon meeting her. (PROSE: A Time & a Place)