VANESSA REDGRAVE, An Autobiography (Arrow, $87). LOOK for an actress who is quintessentially ''British'' and the gaze falls on the strong, willowy figure of Vanessa Redgrave. The features - not pretty, not beautiful but handsome - look out thoughtfully from the cover of her new autobiography suggesting a feeling intellectual, a brave woman. A grave English rose. And it is more or less true. As the blurb has it, Redgrave has played a leading role in Britain's cultural life for almost 40 years. She is known as one of the great stalwarts of both stage and quality film, the fourth generation star of ''The Redgraves'', that renowned family of thinking thespians. In addition, she has been both praised and vilified as one of her profession's few social and political activists. It ran in the family: father Sir Michael Redgrave was active in actors' union Equity, and, having grown up under the threat of fascism, a stalwart socialist. Sir Michael obviously cast a long shadow over Redgrave and is a venerable presence throughout the book. In his day he was criticised as an ''intellectual actor''. ''Perhaps it never occurred to those critics that only an actor who can think can also feel,'' Redgrave wrote, clearly adopting her father's ''method''. Much of the book concentrates on Redgrave's struggle to maintain her own social activism while advancing her career. It was a tricky balancing act. The book tells of how her Trotskyist Workers' Revolutionary Party base was raided by the police in 1975, and how she lost job contracts because she was deemed too controversial. As the party's candidate in the East End she warned in her election address about plans for a military dictatorship in Britain as a strong-arm reaction to the economic chaos and power of the unions in the '70s. Most memorable, however, was her campaign against Zionism and support for the Palestinians which started with the filming of Julia. The distinction between her acceptance of Judaism and her fear of Zionism never saved her from the wrath of the entertainment establishment, however. The drama culminated in her politicised acceptance speech at the 1977 Academy Awards where she was voted best supporting actress for Julia alongside then fellow actress-activist Jane Fonda. The difference is where Fonda is deemed to have ''sold out'', Redgrave has remained outspoken right up to her push for a peaceful solution to the Iraqi invasion of Kuwait which won her international headlines such as ''Vanessa supports Saddam Hussein''. Redgrave was careful to be well up on her facts and studied Marxism alongside the mechanics of her craft but there are many moments in the autobiography when she comes across as an undeniable ''Luvvie'' in the British thespian mould. During the Hungarian crisis, for example, she went to pack clothes for the refugees pouring into Austria: ''I worked with the other volunteers from first thing in the morning until late at night, with a plate of goulash for dinner at midday''. While giving little away about her feelings towards her equally turbulent private life, she is emotive in her selective descriptions of it. When pregnant, she hurled herself ''into the rollers and was picked up and rolled over and over. I thought: 'My baby and I are one, tumbling in the water head over heels'.'' As she was giving birth, husband director Tony Richardson (from whom she later separated), comforted her by saying: '' 'You look beautiful, you look like [Italian actress] Monica Vitti'. I knew he thought the world of Monica Vitti, and so did I, so my morale soared immediately.'' Despite the theatrical delivery, Redgrave's book is finally inspiring as an honest account of a woman with a conscience who has stuck with her convictions, despite the controversy and backlash. Moreover, just as she is seen as a cultural representative for the ''Best of British'' over the years, her autobiography is also a highly evocative account of the political changes and underhand manoeuvrings at work in Britain and globally over the last half century.