A few months ago, Suffolk police stopped me for driving over 30mph. My excuse that East Anglia was so flat it was impossible not to break the limit did not wash, and they sent me on a speed awareness course. Very good it was too. After surveying the human cost of bad driving, I resolved never to speed again. Unfortunately, the instructor was over-fond of his own voice and his lecture went on for hours. "I hope he winds up soon," I whispered to the woman next to me. "I am meant to be speaking to the National Secular Society."

She was a little astonished and a little amused. "A National Secular Society? Why does Britain need a National Secular Society? Surely the secularists have won?"

It can feel that way. The number of people who say they have no religion jumped from 15% in the 2001 census to 25% in 2011. If the remaining 75% were believers, this leap in free-thinking would be significant but not sensational. But those who say they are religious are not faithful to their creeds, or not in any sense that the believers of the past would have recognised. Church attendance is in constant decline. Every year that passes sees congregations become smaller and greyer. As striking as the fall in religious observance is the public's near total disregard for the teachings of the clerics and prelates, who could once claim to be society's moral guides.

To cite the most striking example, a popular liberal prejudice keeps anti-Catholicism alive by picturing Catholics as automatons who blindly follow the teachings of the Vatican. There is no evidence to support it. A poll just before a papal visit in 2010 found Catholics took no more notice of the Pope than anyone else did. Just 11% of Catholics agreed with the church that doctors should perform abortions only if a woman's life was in danger. Just 4% supported Vatican teaching on contraception.

When millions of people tell the census takers they are "Christians", therefore, they are muttering the title of a childhood story they only half remember. What is more, their spiritual "leaders" know it. Long before the census figures were in, you could hear the screams that always accompany ideologies and institutions history is leaving behind.

At one point in the debate about civil gay marriage, the bishops of the Church of England became so demented with fury they implied that we lived in a theocracy with clerical vetoes over democratic decision-making. "Many, within the churches and beyond, dispute the right of any government to redefine an ages-old social institution," they huffed. Meanwhile, the higher regions of the Catholic church and lower regions of the Tory party proved that they were gripped by paranoia – which, I am sure I don't need to tell you, is another classic symptom of intellectual collapse. Joseph Devine, the Catholic bishop of Motherwell, told David Cameron that his support for gay marriage risked turning him into a modern Nero. Just in case his listeners were in any doubt that he was referring to Nero's persecution of Rome's Christians, the bishop added: "I suspect it is only a matter of time before you go one step further and outlaw the teaching of Christian doctrine on sexual morality."

A modest proposal to allow homosexual equality before the civil law – not in churches, mosques, temples and synagogues, which will remain free to enforce what tired taboos they choose – produced an immodest explosion of self-pitying rage. When you consider its impotence as well as its excess, it is easy to agree that there does not appear to be much call for secular campaigners in Britain.

Until you glance at how we are governed. The International Humanist and Ethical Union has just issued a grim report on the legal restrictions of freedom of thought, conscience and religion around the world. Britain has a shamefully long entry, because while everything is changing in British society, nothing is changing in the British establishment. England still has a "national" church – even though in 2010 its average weekly attendance was down to 1,116,100 (or 1.8% of the nation's population).

Twenty-six Church of England bishops are automatically granted seats in the House of Lords to support or oppose any legislation they please. On top of the decaying heap sits Elizabeth II: a grumpy priestess-queen, who in theory at least is the state religion's "supreme governor".

In the education system, almost one-third of state schools are run by religious authorities (and Michael Gove will ensure that number will rise). Atheist writers complain that they indoctrinate their captive audiences. I have to say that the church attendance figures, the British Social Attitudes survey and the census suggest that, if religious schools are propagandising, they are making a poor job of it.

The need for the British to enjoy equal rights to full citizenship strikes me as firmer ground for objectors to stand on. By what right do religious bureaucrats tell parents, who have paid their taxes and obeyed the law, that their children cannot attend a state-funded school because they are not devotees of the required sect? How can Britain criticise religious discrimination in other countries when it provides exemptions that allow religious schools to hire, discipline and fire teachers because the church disapproves of their beliefs or sexual orientation or marital status?

Challenging the growing gap between official Britain and the real Britain will not be a painless process, as the outrage over the coalition's proposals for gay marriage demonstrates. The argument for doing so with vigour is almost identical to the argument for allowing the widest possible freedom of speech. John Stuart Mill claimed in On Liberty that knowledge and self-knowledge make the individual happier – "better to be Socrates dissatisfied than a fool satisfied".

I can see no way of proving that allowing free debate proves happiness. It may well be that people are happier when their illusions and taboos remain intact. But if you prevent challenges to their beliefs, you are not treating them as adults; you are patting them on the head and saying that they cannot handle robust debates – infantilising them, in short. What applies to individuals applies to countries. Facing up to the truth about religious decline, and adapting our institutions accordingly, will doubtless cause pain to some. But it will allow Britain to become an honest and grown-up country that meets the first requirement of maturity by seeing itself as it is.