Slightly over one-third (38%) of the 3,879 people polled for the British Social Attitudes report described themselves as Christian, down from one-half (50%) in 2008, and nearly two-thirds (66%) in 1983.
Conversely, those identifying as Muslim increased exponentially - up from 1% in 1983, rising to 3% in 2008, and 6% in 2018.
The findings represent the first time the percentage of those describing themselves as Christian dropped below 40% since the survey began in 1983, although those identifying as no denomination Christian increased from 3% in 1983 to 13% in 2018.
More than half of all people polled (52%) said they do not belong to any religion, up from nearly one-in-three (31%) in 1983.
The report by the National Centre for Social Research, published on Thursday, said: "The past two decades have seen international conflict involving religion and domestic religious organisations, putting themselves at odds with mainstream values.
"We find a dramatic decline in identification with Christian denominations, particularly the Church of England, a substantial increase in atheism and in self-description as 'very' or 'extremely' non-religious ... but tolerance of religious difference."
The data shows 11% of those with a faith attended a religious service at least once a week, a rate which has remained stable since 1998.
Half (50%) of those polled said they never pray, up from 41% in 2008 and 30% in 1998, although those who pray "several times a day" is up from 5% two decades ago to 8% in 2018, the data shows.
Almost two-thirds (63%) or Britons polled agreed that religions bring more conflict than peace, while 13% disagreed.
The data also showed 51% of those polled "feel positive" towards Christians, compared with 30% for Muslims.
Similarly, 4% of people have negative thoughts about Christians (level with Buddhists), compared with 17% for Muslims.
The report said data offered "compelling evidence that the process of secularisation continues unabated".
It added: "Britain is becoming more secular, not because adults are losing their religion but because older people with an attachment to the Church of England and other Christian denominations are gradually being replaced in the population by unaffiliated younger people.
"To put it another way, religious decline in Britain is generational - people tend to be less religious than their parents, and on average their children are even less religious that they are."
Responding to the findings, Andrew Copson, chief executive of non-religion charity Humanists UK, said: "For the third year in a row, the British Social Attitudes survey - the gold standard in reliable data on our society - has shown a majority of Brits are non-religious.
"With these trends set to continue, policy-makers in every field, from education to constitutional law, to health and social care need to wake up to such dramatic social changes, particularly the rise of the non-religious and the decline of Christianity."
Stephen Evans, chief executive of the National Secular Society, said the figures showed "the need for a serious rethink of the privileges granted to religion in Britain".
He added: "Britain's constitutional settlement and public policies should catch up with the opinions of its population."
Dave Male, the Church of England's director of evangelism and discipleship, said: "Times have changed and for many people ticking a box marked 'Church of England' or 'Anglican' is now an active choice and no longer an automatic response.
"In spite of this, the Church of England remains at the heart of communities with millions of people reached in their daily lives through our ministry and our message of the Good News of the Gospel.
"We are living in an era of rapid social change - but people are still searching for meaning and answers to life. Only this weekend, the General Synod heard that as many as 5,000 new congregations, mission communities and outreach initiatives have been set up in the past 15 years attracting a majority of people - 60% - who have not been churchgoers before."
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