Goddard made early television appearances in Australia, including episode 100 of Homicide ("The Traveller", 1966), and the ABC drama play Romanoff & Juliet (1967), and a brief (non-speaking, uncredited) appearance in the feature film They're A Weird Mob (1966). However, she is best remembered in Australia for her role as Clarissa "Clancy" Merrick in Skippy the Bush Kangaroo in which she appeared in the first two series and 48 episodes.
After returning to the UK in 1969 as an adult, she was cast as Victoria Edgecombe, the character created by Terence Brady and Charlotte Bingham in Take Three Girls (1969), and then its sequel Take Three Women (1982). She also had a supporting role in the 1972 film Ooh… You Are Awful, starring Dick Emery. Her career breakthrough was as April in The Brothers (1972–76), which also featured her first husband, Colin Baker. She appeared as Jocelyn in National Pelmet, the Series 2 opener of critically acclaimed drama Minder.
A comedy role alongside Donal Donnelly in Yes, Honestly (1976–77), by Terence Brady and Charlotte Bingham followed, as did a role, with Christopher Biggins, in a BBC1 sitcom Watch This Space (1980), by Ronald Chesney and Ronald Wolfe. This was followed by Pig in the Middle (1980–83) also written by Terence Brady and Charlotte Bingham.
Goddard was one of the 'explorers' who were evaporated in a (now missing) episode of the BBC science fiction quiz programme The Adventure Game (1980), played a space pirate in the Doctor Who story Terminus (1983), and appeared in Roll Over Beethoven (1985), opposite Nigel Planer. She also played a humanist in the 1988 biographical film Testimony, starring Ben Kingsley. She then appeared in Woof!, a Children's ITV programme first broadcast in 1989. Her third husband, Producer and Director David Cobham, created this series. She had earlier appeared in the TV adaptation of Brendon Chase, also produced and directed by Cobham.
Goddard's first marriage was to former Doctor Who actor Colin Baker. Their son, Thom, is a 20th Century Fox Director. She also dated former Doctor Who companion Frazer Hines (who appeared with Baker in the story The Two Doctors). In 1981 she married pop star Alvin Stardust. She was married to Producer and Director David Cobham. Goddard's daughter from her marriage with Stardust, Sophie Jewry, was critically injured at the age of two months after she fell down a set of stairs and suffered a severe fracture of the skull. She later recovered from her injuries.
She was the subject of This Is Your Life in 1984 when she was surprised by Eamonn Andrews.
Goddard lives near Dereham, Norfolk, in a home full of rescued animals. Goddard also works with the RSPCA amongst other charities. Goddard suffered and recovered from, breast cancer in 1997.
She later had a recurring role as Philippa Vale in Bergerac and alongside Dawn French and Catherine Tate in Wild West (2002). In 2007 she appeared in the Midsomer Murders episode "A Picture of Innocence", reuniting her with Bergerac star John Nettles. In 2012 she had a cameo role in the all-star comedy film Run for Your Wife, and in 2013 she toured with the official Agatha Christie Theatre Company in Go Back for Murder, an adaptation of the book Five Little Pigs.
In September 2016, Goddard played the guest role of Gloria Francis in the BBC1 drama series Casualty.