Michael Rudman does not fit the stereotype of the American Jewish director. He is not small and bespectacled and he is not from New York. Rudman is tall and his Texan accent is largely undiminished by more than half-a-century in the UK. And, as we chat in his Chelsea sitting room, it would certainly be easier to imagine him in a stetson than a kippah. A star-studded acting and backstage cast is remembered in his new memoir, I Joke Too Much, which has considerable Jewish interest. For example, Rudman had the idea that Death of a Salesman, a show he ultimately directed three times, should be a Jewish play and he discussed this with the playwright, Arthur Miller.

"Miller wasn't at all sure whether he wanted it to be seen as a Jewish piece," Rudman recalls. "But I felt that a lot of the speech in the play had the rhythms of the Old Testament. It was just a flavour really - a way of seeing the world and, of course, the writer was Jewish." He recruited Warren Mitchell to play the main role of Willy Loman and he remembers with a combination of amusement and pride that all five actors on stage for the curtain call at the National were Jewish.

He had a spirited relationship with Mitchell who, like Miller, was unsure whether to play the role as Jewish. Rudman laid down the law. "I told him that I had three conditions. The first was that he was not allowed to complain about the money, the second was that he had to play it Jewish and the third was that he shouldn't shout." He accepted the part but then complained about the money, shouted in rehearsals and did not want to play Loman as Jewish. "Warren has a tendency to be against everything you tell him but he did an excellent job in the play."

Mitchell was not the only feisty Jewish leading man to portray Willy Loman in a Michael Rudman production of Death of a Salesman. When the play went to Broadway, Dustin Hoffman took the main role and Rudman remembers an unusual lunch with the star.

"I met Dustin at a restaurant and he was sitting there in a dress and a wig. He was filming Tootsie at the time [in which Hoffman played an actor who found work by dressing as a woman] and he wanted to know if they would recognise him. Well it was a very busy restaurant and they didn't pay any attention to him at all."

Working with Hoffman was a pleasure, he adds. "The whole experience was thoroughly satisfying and financially rewarding. I mean, when you work with an actor like that, compared to most of them it's like going from driving a Morris Minor to driving an Alfa Romeo. Just a little bit of gas and it goes."

Born in Dallas, Rudman was brought up in a Jewish family but not in a religious environment. He remembers going to synagogue on the High Holy-Days but did not observe any of the other festivals. He did not have a barmitzvah but he did attend B'nai B'rith meetings as a teenager - an experience he says was crucial in his future development as a director. "It was terribly important to me. For one thing, it enabled me to control a room. I would say it was as important to me as school."

His life took a more Jewish turn after he started a relationship with actress Felicity Kendall in the 1980s. When they married, she converted to Judaism and took the whole thing very seriously. In fact, Rudman says that it was down to her that their son Jacob had a barmitzvah. "Felicity was very keen on it and when Felicity is keen on something, it tends to happen."

Jacob also had a brit milah and to make up the numbers for a minyan, Rudman invited Michael Winner, who arrived with his non-Jewish partner Jenny Seagrove. "He told me that he had fully briefed Jenny about the bris." When drinks were served after the ceremony, Seagrove asked, in a very loud voice: "When do we eat the foreskin?"

Rudman first became seriously interested in the theatre when he attended college in the US. Before taking up a place at Oxford, he spent some time in Paris, where he discovered his passion for directing. "At college, I wanted to be an actor but realised quite soon I couldn't. While I was in Paris, I did a reading of a Brecht play. The guy directing it seemed a bit hopeless and I thought I could do better than him. So, the next time, I put together a play.

"I was actually thinking that maybe I shouldn't go to Oxford but rather try to make it in theatre somehow. But then I met an English guy who told me that, if I wanted to be a director, Oxford was the best place because that's where they all start. He was right. My first college production was reviewed in The Times."

His career continued with a stint as artistic director of the Nottingham Playhouse, followed by a period at the Traverse in Edinburgh and a triumphant few years at the Hampstead Theatre. During his time there in the 1970s, he decided that the company should not be scared to do different work. He decided to produce a piece about a Victorian man with a grotesque facial deformity. It was called The Elephant Man.

He also had another left-field idea. He had heard of a rather unconventional, bearded young director who came up with plays completely through improvisation. Given that the theatre was then running £11,000 under budget and this money would have to be paid back to the Arts Council if not used, he decided to take a chance on the director - Mike Leigh. The result was Abigail's Party. "The damned thing was a huge hit," Rudman laughs. He went on to enjoy massive success as head of the Cottesloe Theatre at the National, but his career hit the buffers for a while when he took on the job of artistic director at the Chichester Festival Theatre.

"I was arrogant and optimistic - a bad combination. It was also far too much work to do. I had no administrative help and I was trying to direct three plays and produce 10 more. It was beyond me." It was at this time that his marriage to Kendall broke down, although they have since revived their relationship. He says that his time in theatre has been hugely enjoyable and on the whole a lot more straightforward than you would imagine. He has also been gifted a huge reservoir of stories through encounters with legendary figures like Samuel Beckett, Neil Simon, John Cleese and Rex Harrison.

Having said that, when he originally produced a draft of his book, one editor was less than impressed. "He said to me: 'Life must be more than just a series of anecdotes.' To which my answer was: 'Are you sure?'"

'I Joke Too Much' is published by Capercaillie Books, £12.99