Before becoming an actress Padbury took ballet classes but these came to an end due to her flat feet. She replaced ballet with Saturday morning drama classes with a strong emphasis on elocution.
Padbury came to prominence in 1966 when she joined the cast of the long-running ATV soap opera Crossroads after she came second in the television talent contest Search For A Star. For her initial song in the contest she chose "(When I Marry) Mr. Snow" and made the unusual decision to sing a capella. Afterwards, the guest celebrity, Stubby Kaye, praised her very highly and predicted that she would go far, somewhat to the embarrassment of the presenter, since at that point, no one contestant should have been singled out. In Crossroads, she played the role of Stephanie "Stevie" Harris, foster daughter to the show's main character, Meg Mortimer (Noele Gordon).
She was cast as the Second Doctor's new companion, Zoe Heriot, in Doctor Who in 1968. She became very close to her co-stars Frazer Hines and Patrick Troughton, the latter playing the Doctor. Padbury tells many fond stories about the practical jokes they would play on each other during rehearsals.
Her connection with Doctor Who after she left the programme (at the same time as Hines and Troughton) was not quite over. She appeared in Doctor Who and the Daleks in the Seven Keys to Doomsday (1974), a stage play at the Adelphi Theatre London based on the television series, in which she played a companion named Jenny, opposite Trevor Martin as the Doctor. She then made an appearance, again with Hines and Troughton in Doctor Who's 20th anniversary story, The Five Doctors.
Other roles include co-presenter of the second series of Score With The Scaffold. She appeared in three series of the children's television adventure programme Freewheelers playing the part of Sue Craig. She made a series of appearances in the British soap opera Emmerdale (then known by its original title Emmerdale Farm) coincidentally opposite Frazer Hines, one of the major stars of that show.
Her film appearances included a brief role in Charlie Bubbles (1967) with Albert Finney, and Piers Haggard's cult British horror film The Blood on Satan's Claw (1970) as the unfortunate Cathy Vespers. Coincidentally, she appeared alongside actor Anthony Ainley who a decade later would take the role of The Master in Doctor Who, including the above mentioned episode, The Five Doctors.
In an interview with Doctor Who Magazine, Padbury explained that she no longer appeared at Doctor Who conventions nor spoke about her time on the programme, as she felt she no longer had anything new to say about her time in the show. However, following her retirement she returned to the convention scene and was a guest at Gallifrey One in 2009 where she spoke about how she first met new Doctor actor, Matt Smith.
She is now retired and is living in France, having previously been a theatrical agent with Nicholas Courtney, Colin Baker and Mark Strickson, all former Doctor Who actors, amongst her clients. She discovered Matt Smith at the National Youth Theatre.
Padbury attended Alcester Grammar School in Warwickshire. Padbury was married to Melvyn Hayesfrom 1974 to 1987, with whom she had two daughters, Joanna (born 1974) and actress Charlotte (born 1977).