Good on David Cameron – not words I'm accustomed to writing – for kickstarting a debate that needs to be had. A prime minister publicly talking about his faith will inevitably be met by an avalanche of cynicism, provoking reactions ranging from passive eye-rolls to full-on rants at the radio. But I'm sure his Church Times piece (republished in the Guardian) was not intended as a last word, and in that spirit, let me respond: for the good of believers and heathen alike, it's time for church and state to divorce.

I'm not going to quibble over Cameron's declaration that Britain is a "Christian country": it's just a statement of fact. Because of the bond between church and state, we are officially a Protestant nation – in contrast to, say, a formally secular country like the United States, where the founding fathers declared a "wall of separation between church and state". Bishops sit in the House of Lords, making Britain the only nation outside Iran to have unelected clerics in the legislature. One in four primary and middle schools are run by the church, and – unlike any other western nation – all state schools are legally obliged to have a daily act of "collective worship".

But let's face it, this is an anachronistic set-up. While nearly six out of 10 Brits declared themselves to be Christians at the last census, in 2011, the numbers are in steep decline: in 2001, the figure was 71.7%. Many are rather passive believers: only one in 10 of us attends church each week, and polls suggest just 31% believe in Jesus's resurrection. Those reporting that they have no religion have surged: from less 15% in 2001 to over a quarter in 2011. Britain is ever more religiously diverse, too. One in 20 Brits is Muslim; the number of Hindus is surging towards a million; and over a quarter of a million of us are Jewish. We are a Christian nation in name only.

Calling for church and state to go their own way has nothing to do with a believer-baiting, crusading form of atheism. Personally, I find myself having a large degree of respect for the church. Regular church-goers may remain disproportionately the "Tory party at prayer", but Anglican leaders have often made a better fist of opposing pernicious Tory policies than the official opposition.

When Lord Runcie – the Archbishop of Canterbury under Margaret Thatcher – commissioned a report into the plight of the inner-city poor, an anonymous senior Tory denounced it as "pure Marxist theology". Ed Miliband could have learned a thing or two from Rowan Williams when, in 2011, the archbishop guest-edited the New Statesman and launched a welcome attack on "radical, long-term policies for which no one voted". Whatever happens, I hope church leaders continue to speak out for social justice.

People's private religious beliefs should be respected – but they should be exactly that: private. Faith schools, for instance, fuel the segregation of children according to the religious convictions of their parents. Let people celebrate their beliefs in their home, in their places of worship, out in the streets if they so wish – but public spaces should not be promoting religious beliefs in this ever-more diverse nation. It is wrong for the church to be able to interfere in matters of government; and it is equally wrong for the state to be able to stick its nose into the church, too. Disestablishment would set both church and state free.

Committed Protestants are an integral part of Britain's national fabric, but giving special privileges in law to any section of the community is a throwback to an era that has long since passed. This is a nation of many beliefs and of no beliefs. It's time we officially recognised it, and came out as the modern, secular nation we really are.