By Terry Sanderson, president, National Secular Society

We've argued for a long time that the establishment of the Church of England as an arm of the state is unsustainable in a modern, diverse society. Last night's vote at the General Synod to reject women bishops simply reinforces that opinion.

Although as secularists we would defend any church's right to make its own rules (so long as they are within the law and don't affect people outside its ambit), in the case of the Church of England it is different.

This is a church "by law established", a status that brings with it many privileges that are denied to other denominations and religions.

There is no denying that the Anglican Church has had a profound influence on the history and development of this nation. But then, so did steam trains and we did not hesitate to get rid of them when they had outlived their usefulness.

The world has changed profoundly since the Church of England was created, and it is time for us to accept that change is needed. If we don't expect our railway carriage to be pulled by Stephenson's Rocket any more or go to America in a Zeppelin, then we shouldn't imagine that there are not better ways to order our constitution to take account of shifting demographics and progress in science and political thought.

Britain has become a society of many religions, but mainly a nation of no religion. This secularising process has brought into being laws that would never have been even considered if the Church was still in charge. Abortion, homosexuality, contraception, suicide, cremation – all were illegal for centuries on the orders of the Church. All have been legalised by a society that has been gradually rejecting religious dogma for over a century now.

Chief among these progressive laws is the Equality Act, which makes every citizen — religious and non-religious, male or female, black or white, straight or gay, disabled or able-bodied — entitled to the same rights. The Church of England has just set itself against this.

As an Established Church, its legislation has to be approved by our elected parliament. Usually this is just a formality, but with this decision there might be resistance in parliament, which has ruled through its own legislation that women must be treated equally and barriers must not be placed in their way.

If the Church of England wishes to continue with its privileged position in relation to the state, it must change its ways. But there are stronger reasons for its disestablishment – the first being that its supporters have voted with their feet and abandoned it in droves. It is now a tiny denomination, but still claims to speak for us all. With this decision it shows that it speaks for only a small group of conservatives who are out of step with the direction of society.

This morning on the BBC Radio 4 Today programme, the Archbishop of York, John Sentamu, defended establishment because "the Chief Rabbi says it keeps religion at the forefront of the nation".

Well, the Chief Rabbi represents even fewer people than the Archbishop of York.

The Church of England has now shown itself to be an irrelevance, a nuisance and an embarrassment. It is well past its sell-by date and its establishment even more so.