Political hatred and division in the UK is probably worse now than during the Brexit referendum, when Jo Cox was murdered, says Kim Leadbeater, Cox’s sister who is now also a Labour MP.

Speaking to the Guardian’s Today in Focus podcast Leadbeater, who was elected to the same Yorkshire seat held by Cox in a 2021 byelection, said everyone in public life had a responsibility to try and ease tensions.

Referencing the response of some politicians to the murder of Henry Nowak, which was followed by disorder in Southampton, Leadbeater said people should remember that those calling for division were “in the minority” but were very vocal.

Other people, she argued, “have got a duty to drown them out and tell the good stories of this country”.

“After Jo was killed, there was a period where people said all the right things and said: we need to do things differently, we need more compassion, we need more understanding,” said Leadbeater in an interview to mark the 10th anniversary of Cox’s murder by a far-right terrorist on 16 June 2016.

She said: “And it was very short-lived. And sadly and regrettably, I think over the last decade, if anything, things are worse. And I think we have to be honest about that.”

With the anniversary approaching, Leadbeater said, it was time to “have a look at how we can change that narrative”.

In comments marking 10 years since Cox’s death, Keir Starmer said the values she had lived by – that “we have far more in common than that which divides us” – were being tested anew.

He added: “At a time when those values are being tested, her legacy feels as vital and urgent as ever. The best way to honour her memory is to stand firmly against hatred and division, to bring communities together, and to show, through both big acts and small, the compassion, decency and solidarity that define our nation at its best.”

Leadbeater said the responsibility for that change lay with “everybody … including politicians and people in public office”.

“We have a voice,” she added. “We’re very lucky to have a voice and to have a platform. But with that voice and with that platform comes a very significant level of responsibility.

“Recently we saw the horrific murder of that wonderful young man, Henry Nowak, and we saw his family’s response, and they pleaded with people: please do not allow Henry’s murder to be used to divide communities.

“I’ve been in that position, and I know what that feels like. It is unbelievably painful. But what you do not want to see is more anger and more hatred and more division on top of what you’re already going through. Then the opposite happened. Only from certain quarters, though. You’ve got to remember: those voices who are sowing the division are in the minority, and it doesn’t always feel like it.”

“They are very loud. But the rest of us then have got a duty to drown them out and tell the good stories of this country, call out bad things where they happen.

“Absolutely, be angry. I’ve got no problem with people being angry. I am really angry about what’s happened to my life. I’m pretty furious, to be honest. But you then have a choice what you do with the anger. And you can use that anger for good. You can use it to make a difference.”

Cox was 41 and had been an MP for just over a year when she was fatally shot and stabbed by Thomas Mair, a rightwing extremist, before a constituency surgery in the run-up to the Brexit referendum.

In the interview, Leadbeater recalled that she had been collecting her car from a garage when she received a phone call saying Cox had been attacked.

She said: “I remember getting in the car. My legs were shaking and I just couldn’t stop shaking. And instinctively I knew this was not good. And I don’t know if that’s a sister thing. I don’t know if it’s just an instinct thing. I don’t know what it was, but I just knew straight away.

“I remember saying to my partner, who was saying, as people do: ‘It’s going to be OK, it’s going to be OK.’ And I just remember saying: ‘I just don’t think it’s going to be OK.’ And I sort of knew.”

Leadbeater had not previously been involved in politics, but when Cox’s replacement in the Batley and Spen seat, Tracy Brabin, stepped down after being elected West Yorkshire mayor, she was persuaded to stand for Labour, winning the byelection.

Leadbeater said she had decided to stand after speaking with her parents and Cox’s children, in part because she “did not want our community and our country to be defined by Jo’s murder, because that isn’t what our country looks like and that isn’t who we are”.

The foundation set up in Cox’s name campaigns in part on tackling loneliness, and Leadbeater said that with people like Mair, it was important to take account of what she called “the intersection between extremism and loneliness”.

This, however, should not be used as a reason to avoid challenging extreme beliefs, she argued. “If we reduce Jo’s murder to an isolated act, then we are misunderstanding the context within which it happened. And we are misunderstanding and misrepresenting the views of the individual who killed Jo.

“This is someone who was a far-right extremist. And we have to call extremism out, whatever that looks like. We have to have an honest conversation about that.”