In these dark times the Enlightenment itself can seem in retreat. Fact-free emotion wins over reason and the hard-earned liberalism of centuries is thrown into reverse. Donald Trump and Boris Johnson succeed by flamboyantly disregarding truth. Gwyneth Paltrow disseminates Goopy nonsense, Jeremy Hunt dabbles with homeopathy, and mystical claptrap from crystals to hopi ear candles encroach on the domain of evidence-based medicine. The frightening rise of anti-vaxxers puts at risk the gigantic progress in disease control. Are we heading back to the dark ages?

No, is the answer. Breathe a sigh of relief. These strange irrational phenomena are only marginalia in the onward march of reason. The annual British Social Attitudes survey is the best mirror we have to show us an image of who we are, what we think and how we change over the decades since it began asking the same questions in 1983.

Start with religion, in remarkably rapid retreat. In just a decade the number proclaiming no faith has risen from 43% to 52%, as “secularisation continues unabated”. Back in 1983, the BSA’s first survey, two-thirds of the British called themselves religious. Now declining faith means that 12% are Anglicans, 7% Catholics, 19% another type of Christian, and 9% are of a non-Christian religion including 6% Muslims. Here’s the size of the shift towards outright atheism: a quarter of the public now boldly state “I do not believe in God”, compared with just 10% 20 years ago.

Here are the mechanics of this rapid decline: two non-religious parents will successfully transmit their lack of religion to their children, while two religious parents have only a 50/50 chance of making their faith stick. Encouragingly, the decline in faith is matched by a growing tolerance of other people’s beliefs – which has surely never been more important. Yet almost two-thirds (63%) agree that “looking around the world, religions bring more conflict than peace”. As the researchers suggest, the small downturn in approval of same-sex relationships may turn out to be a blip in the long upward trend of support.

As religion declines, all hail the rise in trust in science. The BSA finds a “strengthening of confidence in science and technology” providing “an alternative way of interpreting and understanding the world”. As your plane takes off, in whom do you trust, God or the engineers? That’s quite a change from 1993, when nearly half thought “we believe too often in science and not enough in feelings and faith”. Soaring confidence in science now sees 85% trusting university scientists “to do their work with the intention of benefitting the public”. As you would hope, as in most matters of reason, the more educated the public becomes, the more it trusts in science, with younger, better-educated generations more rational than older generations who largely missed out on post-school learning.

Reading the runes, the established church can see its future looks grim with only 1% of 18- to 24-year-olds saying they belong to the Church of England. We may miss beloved but vanishing old hymns and find new uses for beautiful empty churches, but for how much longer can the C of E hang on to its purchase on power? When will Thought for the Day start including secular thinkers? What are 26 bishops doing in our legislature, making us the only democracy with a theocratic element? True, the men in frocks don’t look out of place in the whole creaking edifice of the House of Lords, with its 92 hereditaries re-electing themselves from Burke’s Peerage. But the high number of religious members of both houses is wildly out of kilter with the wider population.

Prayers in parliament may be no more than an arcane ornament, but the impact of religion on policy is immense, as campaigned against by Humanists UK, of which I am vice president. For decades opinion polls have shown more than 80% of the public strongly in favour of assisted dying, the right for terminally ill people to die peacefully when they have had enough, but time and again parliament refuses. The most impassioned opposers often hide their faith to make their arguments more convincing to a secular country: much of palliative care is dominated by Christians who resist the right to die for faith reasons.

For a third of state schools to be run by the religions is an affront: their subtle social selection is the draw that brings young parents (briefly) to their knees in the pews to get their children into church schools. The segregation of children by faith is getting worse – a dangerous trend in a world of populist politicians stirring up race hate. This country’s firmly secular values need to be upheld against the religious resistance to sex and relationship lessons in over-segregated schools. The right to religious freedom doesn’t supersede national education values.

As religion wanes, so too does party political identification: only 35% now claim a party identity. Brexit passions are the “new political and social faultlines”, far exceeding party loyalties, with 75% “strong” or “fairly strong” leavers or remainers. Labour needs to note that more than twice as many plant their flag on the Brexit divide than on Labour vs Tory turf, undermining old loyalties. Brexit, say the BSA researchers, is a “striking illustration of the power of identity in modern Britain”.

This visceral Brexit war between old and young, between regions and outlook, has often felt like a conflict between reason and unreason, between economic fact and emotional national identity. But the BSA report reassuringly finds that beneath the surface of our present turmoil, superstition and unreason are on the retreat, with the onward march of trust in evidence-based scientific truths. When it comes to the great climate question and whether life on Earth will survive, that augurs well. Not prayers but only human agency can save us.

• Polly Toynbee is a Guardian columnist