This proportion is the highest ever, up from 48 percent in 2015 and 31 percent in 1983 when the British Social Attitudes survey was begun by the independent National Centre for Social Research.
The trend is evident across all age groups but is particularly marked among young people, with 71 percent of 18- to 24-year-olds surveyed in 2016 saying they had no religion, up from 62 percent the previous year, said the survey out Monday.
"This increase follows the long-term trend of more and more of us not being religious," said Roger Harding, head of public attitudes at the research centre.
"The differences by age are stark and with so many younger people not having a religion it's hard to see this change abating any time soon.
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"The falls in those belonging to the Church of England are the most notable, but these figures should cause all religious leaders to pause for thought."
However, the proportion of Catholics has remained relatively stable, at around one in ten.
Six percent of Britons said they follow a non-Christian faith, down from eight percent in the previous year but up from two percent in 1983. The survey did not go into more detail.
The 2016 survey involved interviews with 2,942 people, who were asked: "Do you regard yourself as belonging to any particular religion.