A few years ago a member of a Progressive community in north London put a new idea to it. She was happy to turn up to synagogue on Saturday, but worship didn't do it for her. High choral or happy-clappy guitar, she wasn't searching for any kind of service, but she did have a serious interest in Jewish study.

So she suggested starting a monthly literary group on a Shabbat morning. It might look at a piece of Amos Oz or the prophet Amos. But whereas many synagogues these days offer an alternative minyan in parallel to the main service, this was not a minyan. The rabbi supported the experiment, but other members felt it divisive and it ran only briefly - although it continued outside as a private group.

Maybe the initiative was ahead of its time, but we might expect more like it for one good reason; there appears to be a growing number of Jews who identify themselves as cultural or secular rather than religious. In his 2012 book, This Is Not The Way, the emeritus rabbi of the Liberal Jewish Synagogue, St John's Wood, David Goldberg, argued that most Jews, even many synagogue-goers, were no longer motivated by belief in God, at least not the commanding Creator of biblical tradition. There was a fourth type of Jew in town, he said, alongside Orthodox, Reform and Zionist - the "Cultural Jew".

Statistics back up his claims. The most extensive recent survey of British Jews, published early last year by the Institute for Jewish Policy Research (JPR) found that nearly a quarter (24 per cent) regarded themselves as secular or cultural rather than belonging to any of the religious streams of Judaism. What is more significant is the trend.

Whereas 40 per cent of those polled were raised as traditional - typical members of the United Synagogue or similar regional congregations - only 26 per cent remained so now. By comparison, only 15 per cent had been raised as secular/cultural but their share of the Jewish community had increased by more than half.

The concept of being Jewish is tied to no specific content

Add to the seculars a further 10 per cent of British Jews who described themselves as "just Jewish" rather than favouring any particular denomination, and the cultural camp probably covers a third in all. Drill down a little further into the figures and you find something more. Asked to rank which values were important to them in their Jewish life, belief in God came just 16th out of 20, cited by barely over half (52 per cent) below support for social justice or working hard. In other words, a fair number of those who profess to be Progressive or traditional do not exhibit a strong conventional faith.

The shift in Britain mirrors what has been happening in the largest diaspora community, the US. In late 2013, the Pew Survey reported that 22 per cent of American Jews said they had no religion and fewer than a third (31 per cent) belonged to a synagogue. Again the trends are telling. Whereas only seven per cent of those born in 1927 or before regarded themselves as non-religious, that proportion had climbed to almost a third (32 per cent) for those born in 1980 and after.

The Pew Survey added new fuel to a growing debate: is American Jewry in a state of transition or disintegration? The pessimistic case was forcefully put by two professors, Jack Wertheimer and Steven Cohen, in an essay in the online American magazine Mosaic last year. Wertheimer teaches at the Conservative rabbinic academy, the Jewish Theological Seminary in New York, while Cohen is a sociologist with a long track record in studying contemporary Jewish society.

According to the Pew data, they wrote: "Jews who identify themselves with the Jewish religion are far more engaged with all aspects of Jewish life than are Jews lacking such an identification. By all aspects, we mean not only such obvious things as synagogue attendance and ritual observance but also connection with Israel, engagement in non-religious organisations, likelihood of giving to Jewish causes and forging close friendships with other Jews."

For example, 69 per cent of Jews by religion gave to a Jewish charity, whereas only 20 per cent of those without religion did so. More than 90 per cent of religious Jewish families were raising their children as wholly or partly Jewish, compared with only a third of non-religious Jews. Depicting American Jewry to be in "deep-seated crisis", they argued that the figures demonstrated the link between religious involvement and Jewish continuity.

A much rosier alternative, however, has been painted by two other academics, who championed life "beyond the synagogue" in an article for the 2012 American Jewish Handbook. Former Board of Deputies demographer Barry Kosmin and Ariela Keysar work at an institute for the study of secularism at Trinity College, Connecticut.

Even before Pew, which came out the following year, earlier surveys pointed to a "general disengagement" from the synagogue among most American Jews, they said. But they saw no reason to despair. Instead, they believed that "the richness and fecundity of contemporary Jewish culture…is more than enough to sustain a purely cultural/secular Jewish identity."

To prove their point, Kosmin and Keysar (the 2Ks) highlighted the multiplying number of Jewish film, book, food or music festivals happening in many American cities. Jewish studies courses at universities have grown to the extent that an estimated two out of five Jewish students take one as part of their degree.

The American Jewish novel has not ended with Bellow or Roth, but a new generation of writers has grown up, including Rebecca Goldstein, Jonathan Safran Foer and Michael Chabon. Jewish humour continues to thrive. A humanist Jewish movement, a deity-free attempt to replicate Jewish congregational life, founded by Rabbi Sherwin Wine in 1969, has 28 groups, 14 rabbis and 10,000 members (admittedly small fry among the six to seven million American Jews as a whole).

Secular Jewish culture, for the 2Ks, has one especially positive feature; not only is it open to Jews of all kinds but also it does not erect barriers to their non-Jewish partners. Its inclusiveness also helps to make it viable. Beyond this, digital media acts as an unprecedented information outlet and connector of people across geographical boundaries.

There may be many ways to characterise secular Jewish culture. (Israel with a Hebrew-speaking society that runs according to the Jewish calendar is a case apart.) But Kosmin and Keysar go for a minimalist definition, specifying three elements; awareness of being Jewish, sense of connection with other Jews, and a concern for Jewish life and issues.

The first thing to note is that their conception of Jewishnesss is highly subjective; it depends on an individual's self-determination of his or her identity rather than any collective norm regulated by an external authority. But more than that, it is Jewishness tied to no specific content.

The worlds of the Liberal and Charedi Jew may seem far apart but they share an underlying religious heritage - the Shema, Kiddush, the blowing of the Shofar at Rosh Hashanah, the use of Hebrew, the public reading of the Torah, the Pesach Seder, etc. Whatever the differences in theology and interpretation between the various religious streams, the basic rituals and the values attached to them have formed the bedrock of Jewish peoplehood for most of history. But the cultural secularism of the 2Ks is a more consumer-driven phenomenon, more a pay-as-you-go kind of Jewish association shaped by individual taste than a sense of communal duty.

Significantly, too, in the diaspora the vast majority of the institutions responsible for the education of children are run by religious groups , whether synagogue classes or Jewish schools. No independent network of secular Jewish education has emerged here - and children's education is mostly in religious hands within the USA as well. Even many of the youth movements which influence British-Jewish teenagers come under a religious umbrella.

"And you shall teach your children" is one of the fundamental principles of the Shema; the transmission of Judaism from one generation to another has resulted from a sustained educational commitment. Adults may be able to dip into the vast pools of knowledge now available on the internet but can digital media take the place of the classroom in teaching Jewish children?

The debates over Jewish identity are more than just food for academics and commentators because they have a practical impact on community decision-making. British Jewry's most expensive single project, the £50 million JW3 centre, which opened in London two years ago, was not styled as an alternative synagogue as such but it was intended to provide a Jewish address for those who sought Jewish experience in the auditorium rather than the sanctuary.

When the community's largest religious body, the United Synagogue, published its strategic review earlier this year, the most striking feature was its recognition of the reality of the growing number of secular Jews. It recommended that synagogues put on more social and cultural events to attract ostensibly non-religious members of the community.

Nevertheless, there was an unwritten assumption in the US report. Synagogues may add to their repertoires with concerts and wine-tasting but these secular extras still take place within a religious framework. Synagogues retain their position as primary centres of collective Jewish purpose. They are the miniatures of the Temple, the scrolls within their ark an echo of the tablets within the Holy of Holies that embodied the Covenant.

Jews may have always been the people of books rather than a single book, but there remained one book above all that they read in common, the Torah; and that was always more than a single text but a whole river of commentaries, interpretations, discussions, rituals, social practices and values that have flowed out of it. The Torah, even though its meaning may be disputed, has proved a unifying thread.

Perhaps a distinction can be drawn between a cultural Judaism that continues to read and to be shaped by the ancient stories and one that regards the Bible as a backwater belonging firmly to the past.

A cultural Judaism that retains not only a sense of history but a connection with Judaism's formative texts may have staying power. But one which turns it back on Judaism's primary source book may lack the roots to be able to renew itself. It may produce spectacular bursts of creativity from time to time but, like a shower of meteors, all too quickly vanishes into the night.