The actress, who was best known for her role in 1968 sci-fi series The Champions, lost her battle with cancer on Sunday (January 12), theatre director and close friend Roger Redfarn confirmed.
Hove-born Bastedo was discovered by Columbia Pictures at the age of 16 and sent to Hollywood to make horror film 13 Frightened Girls.
She later landed the role of Sharron Macready in The Champions, which ran for 30 episodes on ITV between 1968 and '69.
The show, which also starred Stuart Damon and William Gaunt, centred around three agents for a United Nations law enforcement organisation who gain superpowers after a plane crash.
Watch the opening sequence of The Champions below:
Bastedo's other TV credits include an episode of Absolutely Fabulous in 1992 and EastEnders, in which she played Cynthia Marshall between 2008 and 2009. She also appeared in 1967 movie Casino Royale and 1995's Batman Begins.
Bastedo dated stars such as Omar Sharif and David Frost during her Hollywood career. She was married to celebrated theatre producer and director Patrick Garland from 1981 to '84 and again from 1991 to '94. Garland died last April at the age of 78.
A vegetarian and passionate animal rights supporter, she founded the Alexandra Bastedo Champions (ABC) Animal Sanctuary at her home in West Chiltington, West Sussex 30 years ago. The charity aims to "rescue abandoned animals and animals in distress and provide them with care and protection".
She has written autobiography Beware Dobermanns, Donkeys and Ducks, as well as books on caring for cats and dogs.
Actress Liza Goddard and actor Peter Egan are among the stars who paid tribute to Bastedo on Twitter:
My dear friend Alexandra Bastedo died today. A beautiful person who will be greatly missed— Liza Goddard (@LizaGoddard) January 12, 2014
@abcsanctuary Deeply sad. Our dear friend Alexandra Bastedo lost her battle with cancer at 4pm today. A beautiful woman and Animal Champion.— Peter Egan (@PeterEgan6) January 12, 2014