On its website, Habonim describes itself as "a Socialist Zionist Culturally Jewish youth movement". Given that even the Labour Party remains wary of mentioning the S-word, while the term Zionism carries negative connotations, it is quite a bold mission statement. Certainly, the former member and comedian David Baddiel admits "when I first joined, I thought Habonim was very serious and strange".

But at the age of 10, growing up in north-west London in the 1970s, Baddiel recalls, such concerns quickly paled next to his anxiety to keep up with what his older brother, Ivor, was doing. Baddiel attended weekly meetings at Habonim (Hebrew for "the builders") and quickly discovered that, far from being strange, the environment for youngsters was relaxed and fun, with singing, dancing – and girls. "For the lower-middle class, arty, boho end of the Jewish religion, its appeal was as a kind of hippy Jewish scouts."

With its regular outings and summer camps, blue uniform (an informal shirt with a lace-up neckline) and its "miskad", or quasi-military parade, there are certainly parallels between Habonim and Baden-Powell's youth groups. Yet neither the Boy Scout movement, nor the Girl Guides for that matter, share Habonim's extraordinary track record as a hothouse which produced significant figures in the arts and entertainment industry.

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Baddiel's contemporaries in "Habo" included Howie B (Howard Bernstein), the music producer noted for his work with Björk and U2; David Gavurin of the alternative rock group The Sundays; the award-winning film-maker, Jes Benstock; and Baddiel's big brother Ivor, a scriptwriter who works with Dermot O'Leary and Ruth Jones.

But the 1970s were no isolated golden age in the movement's eight-decade history. Habonim in the 1980s nurtured the precocious comedy talents of Sacha Baron Cohen ("I left when I was 15, but Sacha was a big cheese in Habonim and stayed much longer," Baddiel remembers), Dan Patterson and Mark Leveson, co-creators of Mock the Week, and the Bafta-winning producer of Peep Show, Robert Popper. Habonim eventually spread from its UK base to 21 countries, and its Canadian outpost counted among its members Seth Rogen, star of Knocked Up, and a future collaborator with Baron Cohen. Back in the 1940s, Habonim members included the playwright Sir Arnold Wesker, and in the 1950s, the five-times Oscar-nominated film director, Mike Leigh.

This remarkable roll of honour is celebrated in Entertaining the Nation!, a new exhibition at London's recently refurbished Jewish Museum, which examines the high levels of participation by the Jewish community in Britain's cultural life, from Harold Pinter and Sid James through to Marc Bolan and Amy Winehouse. Among the exhibits on display is a picture of the young Baron Cohen, long before Ali G, Borat and Bruno made him a household name, performing in a show with his fellow Habonimniks.

All youth groups aim to help teenagers navigate the choppy waters between childhood and adulthood, and some try to encourage them to discover, in the process, a sense of themselves and their potential. But there was, it seems, something extra that distinguishes Habonim – or, as it has been known since 1980 when it merged with another group, Habonim Dror – that has led to it being labelled a "comedy talent factory".

"That's not how I remember it," reflects David Baddiel. "Because I was younger than the group I was mixing with there – they were my older brother's friends – it represented for me more a chance to learn about fashion and punk and politics, and about how to be a young adult. But it did have this tradition of putting on impromptu shows, and so it was at Habonim that I did my first-ever performance. In the shows, there would be dancing – six girls, all of whom I fancied, plus one rather ambiguous bloke, performing, bizarrely in retrospect, to Elton John's "Funeral for a Friend". And then there would be what we called 'ziggim'. It is the Hebrew word for sketches. We used a lot of Hebrew words in Habonim."

Of that first appearance on stage, Baddiel can only remember that he was joined by Jes Benstock and that together they were "so bad I'm still embarrassed". His brother, Ivor, though, retains a clearer memory of himself "trying to do a Tommy Cooper, being a rubbish magician, and failing completely".

Ivor Baddiel can also trace a definite link between what he does now – writing comedy as part of a larger team – and what he learnt at "Habo" when preparing "ziggim". "It was somewhere that gave us the space and encouragement to be creative. You have to be careful of over-stating it because for many of the people who went on to make it their career afterwards, performing was already there in their family background. But being given the freedom to improvise together as a team was important for me. If you are going to chuck out comedy ideas to a group of collaborators, you have to develop the confidence that you are in a safe place where the others won't rubbish you. Otherwise you will clam up. And I learnt that at Habonim. It was somewhere I could be myself and be funny."

That collaborative, almost anarchic ethos sowed the seeds of something that spread beyond comedy writing. Mike Leigh, whose own parents had met at Habonim, joined in Manchester in the late 1950s. Though he believes that the trademark melancholy comedy of films such as Secrets & Lies and Another Year owes little to Habonim, he freely acknowledges that he owes it a great debt when it comes to his distinctive method of working with actors. "As a writer, I don't achieve much sitting on my own in a room at a desk. I prefer working communally, as a group, with actors, and that, I'm sure, comes from Habonim."

Of Habonim's three founding principles of socialism, Zionism and Judaism, the everyone-is-equal approach arguably can be most readily linked with the socialism. But another of the "comedy talent factory" stereotypes about Habonim is that it allows its recruits to develop a particularly Jewish sense of humour. So does the Judaism also play a key role?

Jem Stein, London Field Director of Habonim, thinks so. "As a small community in Britain, Jews have always had to be creative about how we express our messages and how we pass on our tradition, by keeping it fresh and entertaining. And that included having a sense of humour about ourselves, satirising our situation as a minority community and parodying our own community."

David Baddiel is wary of labouring the connection between Habonim's Judaism and its success in producing comedians. "It is a huge generalisation, but there may indeed be something about being Jewish that means you are 5 per cent outside the cultural mainstream here, and that that can mean you are quite expressive. We are not completely like everyone else. But I don't believe there is a tradition of Jewish comedy in Britain as there is in America with shows like Seinfeld. If it is developing, it has only happened very recently. I was one of the first comedians, for example, to stand up on stage and talk about what it really means to be Jewish."

What would he say was Habonim's part in shaping him as a comedian? Baddiel pauses to consider. "Most of the time for me it was a place to be with other Jews, playing the guitar, performing sketches and trying to get off with girls. In that sense it was inevitably a breeding ground for humour, given how unsuccessful I was at all three."

The socialism in its mission statement may also influence Habonim's reputation for turning out comedians and comedy writers. Politics, after all, often lends itself to satire, while politicians with a quick wit appeal to voters. But politics at Habonim in Mike Leigh's day was anything but a laughing matter. "While my contemporaries were discovering coffee bars, at Habonim we were discussing radical politics. We joined the campaign against capital punishment, for example, and went on the anti-nuclear marches to Aldermaston." That, he says, was the healthy side of the political dimension, "but there were also a lot of speakers from Israel feeding us political propaganda".

Which is where Zionism – the third, and in today's climate potentially most controversial pillar of Habonim – comes in. For Arnold Wesker, whose plays Roots and Chicken Soup with Barley draw on his own Jewish background, the reference to Zionism in Habonim's mission statement has a simple and unchanging meaning: "A Zionist, very simply, is someone who believes the Jews should have a land of their own".

It is the rest of the world, rather than Habonim, that has tried to change and misinterpret the meaning of Zionism, he protests, so that the word can now mistakenly encapsulate a perceived hostility to Palestinian communities in Israel. To emphasise his point, he quotes from the Habonim handbook he was given when he joined at the age of 13 in 1945. "The Movement instils in its members the spirit of friendliness towards all races and creeds and kindliness towards all living creatures."

Wesker illustrates his point by describing some hostile questioning he once faced at an international festival over his links with Habonim. "I was asked: 'Is it true, Mr Wesker, that you were a member of a Zionist organisation and if so can you explain why?' I almost couldn't comprehend the question. 'Yes, I was a member of a Zionist youth organisation called Habonim, which I joined because I enjoyed singing Israeli songs and dancing Israeli dances and the girls were pretty and eager to share kisses.' The reply, though aiming to dismiss the man who'd imagined he'd unearthed a ghastly past, was not without some truth."

From its inception, Habonim was quite openly working to draw young Jews from the Diaspora to what was then the Palestinian Mandate where they could make new lives on utopian, left-wing kibbutzim, egalitarian communities working to transform the desert into citrus groves. The spirit of the kibbutzim – creative, anarchic, making their own entertainment – was at the very heart of the approach taken to all their activities by Habonim groups in the UK. Socialism and Zionism at this stage went hand in hand, and money raised by Habonim in this country funded seven kibbutzim in Israel.

Arnold Wesker recalls from his own Habonim days talks by "people from Israel who came to guide and inform us, not encourage or entice, about what was on offer there, and then left us to make a choice. My first girlfriend did go and settle there, as did many others".

Over the decades, though, that emphasis on settling in Israel appears to have been diluted. By Mike Leigh's day, energies were directed more to recruiting habonimniks to spend a gap year on kibbutzim, using visiting speakers who he remembers as spouting propaganda. By the 1980s, a contemporary describes Sacha Baron Cohen coming to a Habonim meeting in disguise as an Israeli official and giving a humourless, hard-line talk on kibbutzim. It took them 20 minutes to rumble him.

Satire may in that moment have replaced commitment, but the wish to make a practical link between young British Jews and Israel remains a central part of Habonim to this day, Jem Stein reports. Building on their involvement with local community projects in Britain, around 100 teenaged Habonim members each year go to Israel, though increasingly as part of what he describes as "the new kibbutz movement, small communities living together in cities working for social justice".

Stein rejects any suggestion that Habonim's on-going commitment to Zionism has compromised the organisation in today's climate. "Our work is about supporting Israel, but what supporting Israel actually means is a complex question for many Jews who wrestle with the concept of the Jewish state."

Yet there is now undeniably a degree of tension between two of the original three building blocks of Habonim. Zionism, as it is usually portrayed today, and left-wing politics, can make for unhappy bedfellows. Perhaps that accounts for why Habonim is now a smaller organisation. In 2007, it moved out of its large headquarters building on London's Finchley Road and membership nationwide stands at about 600 with groups in Manchester, Glasgow and Leeds as well as London.

While community work is undertaken outside the Jewish community, it also remains true to its commitment to be a Jewish organisation. Yet that has never meant a narrow religious definition of who is Jewish. Ivor Baddiel recalls that in his day "a few members would wear skullcaps and adherence to kosher laws was nominal". At current camps, Jem Stein reports, there is sometimes a religious element, but only when it fits in with what else is happening there.

The essentially non-religious nature of Habonim is, potentially, the final factor that explains its success, over and above other Jewish youth organisations, in nurturing creative folk with the emphasis latterly on comedians. The devout do not, after all, have much of a track record in laughing at themselves, or making other people laugh. Habonim, Ivor Baddiel suggests, stands out in its field because "all the others are straighter or stricter". And in practical terms, he says, past membership can certainly help when you are struggling to make your mark.

"Early on in my career, like many other hopeful writers, I used to turn up at the open commissioning meetings for the Radio 4 comedy show, Week Ending, trying to get one of my jokes included in the script. Dan Patterson was producing at the time, and I remember at the end of the meeting, when he wanted everyone to go, he said 'betorim'. It was the word for 'dismissed' we used at the end of the parade at Habonim. I think I was the only one in the room who knew that, and was able to make that connection!"

Entertaining the Nation! begins at the Jewish Museum in London on 25 May; see jewishmuseum.org.uk