Calls to allow free schools set up by faith groups to select up to 100% of pupils on the grounds of their religion are misguided, especially at a time when the need to prevent radicalisation is in the spotlight. Ministers should reject this approach and instead promote a wider system.

With this in mind, it should be a matter of worry that in Britain today our school system still allows cultural isolation of children. The target the government has set of 500 new free schools is a challenge. But rather than encouraging applications from those who wish to educate only pupils of one faith, ministers should look at the example of schools such as the state sector’s highest-achiever, King Solomon academy. It has an ethnically highly diverse school community owing to its postcode, is open to anyone, and champions secular liberal values alongside outstanding academic results.

We have scores of free schools promoting a faith ethos, yet barely any focused on maths or science and none on humanism. We should be encouraging world-class universities, businesses and community groups of all kinds close to places such as Bradford, Birmingham and east London and elsewhere to create schools committed to excellence for all regardless of religion.

It is also time for the government to end the moral relativism that pervades Whitehall and gives faith groups – sometimes with questionable views – access to money and influence in our education system. I’m not talking only about Muslim groups.

The government should put an end to the special privileges enjoyed by religious schools of all types. Voluntary aided religious schools can ignore the admissions code and select pupils on grounds of faith. They do not face the same requirements as other schools to teach about other religions, and have an opt-out from the Equality Act that has been used to justify gender segregation.

They have their own inspectorates; one, the independent (Christian and Muslim) Bridge, was finally closed in September 2015 after Ofsted found that its inspections “over-emphasise … religious values” and “disguise serious weaknesses in schools”.

Meanwhile, inspections of the Christian Plymouth Brethren schools and Steiner schools, some of which were found not offering science GCSEs but promoting homeopathy and anthroposophy, continue to be overseen by the independent School Inspection Service.

Many faith schools are open and inclusive, but some are not. Even Pope Francis warned recently that such institutions acted to “distance one culture from another”.

We cannot afford the current equivocal approach. Most of all, we need a comprehensive system for all children, acknowledging that in a tolerant society religious groups deserve equal but not special treatment. Faith groups should have the same right as any other to found schools, but should be made to abide by the same admissions code, balanced curriculum requirements and the Equality Act.

When I was working as Michael Gove’s special adviser, it was clear that our education system did not have a strategy to systematically oppose extremism. Despite having a committed education secretary and a highly capable minister in Lord Nash, our efforts in this area were held back. The deputy prime minister, then Nick Clegg, other cabinet ministers and senior mandarins were all unwilling to upset influential faith community interests. While I believe progress has been made since 2014, I profoundly wish we had been bolder, and urge Nicky Morgan and her colleagues to act more decisively now.

Bringing communities together should be the aim of every school and an education that promotes tolerance and inclusivity should be the birthright of every child. These are not British values, but universal ones. They are our most important weapon in the fight against extremism.

Jamie Martin was an adviser to Michael Gove in 2008-10 and 2014

• This article was amended on 26 January 2016. An earlier version said the Plymouth Brethren had been given permission to open a free school. That is not the case.