The Prime Minister has confirmed he and his wife Samantha are considering several state secondary schools for his 10-year old daughter Nancy.

David Cameron, who was privately educated at £34,500-a-year Eton College, said he believes there is "no reason" why British state schools can't provide as good an education as private schools.

If he makes good on his vow, Cameron will become the first serving Conservative prime minister to send his child to publicly-funded school.

In an interview with Good Housekeeping magazine, the prime minister said his family had viewed "three or four" schools in the areas – and that his daughter will have the final say.

"We want to [send Nancy to a state school], I have always said that. We have been round three or four schools in London and had a good look. My daughter has got a very large say in the matter, so she is having a think about what she has seen. But there are some good schools to go to.

"If you pay your taxes you shouldn't have to pay all over again. There is no reason why our state schools can't be among the best in the world, and some of them are. What is exciting is there is this change, not only in practice but also in culture, which is all about excellence and wanting to be the best and wanting to get the best out of every child, and you are now seeing that in more and more schools."

A move to a state secondary school seems possible, given that the Cameron's children currently attend a Church of England state primary school in Kensington.

The Camerons are understood to have looked at The Grey Coat Hospital Church of England School, an all-girls comprehensive academy close to Downing Street. Former education secretary Michael Gove sent his daughter Beatrice, who attended the same primary school as the Cameron children, to the school.

They have also visited Holland Park School – one of the first comprehensives in the UK, where the late Labour MP Tony Benn sent his children – and Lady Margaret School, an academy in Fulham, which is rated "outstanding" by education watchdog Ofsted in 2011.

Education secretary Nicky Morgan chose a state primary for her son. She said: "I think you have more good and outstanding [state] schools. The choice is there. My son is at a good, local village school and there was really no question that was where he went after nursery."

A Downing Street spokesman said: "As with other parents at this time of year, the prime minister and Mrs Cameron are looking at various schools for their daughter to go to next September."