Rishi Sunak has said he would back the creation of new grammar schools if he becomes prime minister, as he clashed with Liz Truss at a Conservative party hustings.

The former chancellor, who attended one of the UK’s most expensive public schools, used his opening speech at the debate in Leeds to say he would create “a Britain where the birthright of every child is a world class education”.

Asked by presenter Nick Ferrari to give a yes/no answer to the question of whether he would bring back grammar schools, he said, “yes”.

“I believe in educational excellence, I believe education is the most powerful way that we can transform people’s lives. But I also think there’s lots we can do with the school system as we have it,” he added, highlighting reforms carried out by Michael Gove when he was education secretary.

Grammar schools were phased out in most parts of the country from the 1960s in favour of the comprehensive system, amid concerns that they entrenched inequality.

Some Conservative MPs have long hankered after their return, despite evidence that they tend to disproportionately benefit the children of wealthier families.

When Truss was challenged by an audience member about the impact of Covid on the schools system, she said, “we should not have closed our schools, and I think it has caused a great deal of damage to our children”.

To tackle the legacy of the pandemic, she suggested there should be more mental health support available for children, and a focus on school standards.

In response to an audience member, Truss also suggested she would instruct schools to provide single sex toilets. “I’ve been very clear that single sex spaces should be protected, particularly for young people, as well as vulnerable people … as prime minister I would direct that to happen, because it’s a difficult time being a teenager, being a young girl, and you should be able to have the privacy you need in your own loo.”

When Truss was challenged by an audience member about the impact of Covid on the schools system, she said, ‘we should not have closed our schools’.

Asked about transgender children, she said, “I do not believe that under 18s should be able to make irreversible decisions about their own bodies that they might come to regret later,” but added, “schools should be sensitive: they can provide additional facilities, but it should not be at the expense of protecting young girls.”

The hustings was the first of a dozen such events organised by Conservative HQ, to be held throughout the remaining six weeks of the contest.

Unlike the previous televised debates, which have featured fiery disagreements between the pair, the event saw Sunak and Truss initially appear separately, with each given the opportunity to make a short speech, and take members’ questions.

Truss, who lived in Leeds for much of her childhood, highlighted her connections with the city, pointing out that her parents still live there, and jokingly apologising to her former teachers after she criticised the school she attended.

“What I think I got from Yorkshire is grit, straight talking and determination: and that, my friends, is what we now need in Downing Street,” she told the audience of Tory members.

Sunak pointed to what he said were the values of his family: “patriotism, service, hard work, aspiration”.

“Family means everything to me – the bonds of sacrifice and commitment that family brings are far greater than anything that any government could ever replicate and we should never forget that,” he said.

During the question and answer session, the candidates were asked to name the best prime minister the UK has had, and both chose Margaret Thatcher.

Truss said, “what I sensed in the 1980s was a growing sense of pride in our country and a growing sense of optimism about our future.”

When Sunak was asked what Thatcher would have made of his policy of increasing taxes, he insisted, “I think she would have responded as I have done by gripping inflation first. That was very much her mantra, was do that first.”

One awkward moment came when Sunak was challenged by one party member, Matthew from West Yorkshire, over his role in the departure of Boris Johnson. “Many people continue to support Boris Johnson who has delivered consistently through treacherous waters, and many people unfortunately see that you’ve stabbed him in the back,” he said.

Sunak replied by highlighting the claim made in his resignation letter that he had stepped down because of policy differences. “I resigned, because the prime minister and the chancellor cannot be in a different place when it comes to economic policy.”

The former chancellor is widely viewed as the underdog, with several polls of Conservative members suggesting Truss has a convincing lead.