More than 20,000 children started at faith schools in England this month, despite choosing secular schools as their first preference, the National Secular Society has said.

The campaign group is now calling on the government to curtail the power religious groups have over state schools and ensure all pupils can go to a secular school if they choose.

However, the Department for Education has described the findings as “totally misleading”.

Data obtained by the NSS under the freedom of information act revealed that 12,311 pupils were assigned to faith secondary schools and 8,333 pupils were assigned to faith primary schools, despite requesting non-faith schools as their first choice.

Just over a fifth of these pupils (4,300) were sent to faith schools they had not included as any of their choices – 2,773 secondary pupils and 1,589 primary. Parents are able to select between three and six options on their school applications.

A total of 21 per cent of those who put a non-faith secondary school as their first choice and did not get it were assigned to a faith school. At primary level, it was 14 per cent.

At the start of January 2017, there were 6,814 state-funded faith schools in England, making up 37 per cent of all state primary schools (6,177) and 19 per cent (637) of all secondaries.

Alastair Lichten, head of education at the National Secular Society, said the figures show children are “having religious pushed upon them against their parents wishes”.

He said the government should stop building new faith schools and “roll back existing religious control over state schools”, or at least ensure every pupil “has the right to a suitable secular school”.

A spokesperson for the DfE said the figures were “totally misleading” and that in the “vast majority” of cases a place at a faith school is only offered if parents have listed that school as one of their preferences.

“We are committed to offering parents and children a diverse education system, which includes the option of faith schools.”

Last year, the government attempted to make it easier for faith groups, specifically the Catholic church, to open new faith schools by reviving its support for voluntary-aided schools. The push was a compromise after ministers refused to lift the cap on faith-based admissions to free schools.

However, the move has so far had limited effect.

Schools Week revealed in March that just 14 bids were received for the new schools. Just one, Hampton Water Roman Catholic Voluntary Aided School in Peterborough, was approved in principle, but the Department for Education said it was working to identify sites for two more.

A spokesperson for the Catholic Education Service said a third of pupils in Catholic schools are not Catholic “and as such Catholic schools remain extremely popular with parents of all faiths and none.”

The Church of England claims not all of its schools are faith schools, because some do not have a formal religious designation. The NSS argues that any school with a religious ethos can be described as a faith school, and so has included all of the Church of England’s schools in its data.