Labour MP Kim Leadbeater, who represents her sister's former seat in Parliament, said threats to politicians' safety and the strain on their mental health meant the UK's democracy was in a "dangerous" place.
In a further sign of the strain being felt in Westminster, Tory MP Elliot Colburn said MPs across the House had attempted to take their own lives.
The MPs were speaking to the BBC Radio 4's show Broken Politicians, Broken Politics.
Cox was murdered in 2016 by a right-wing extremist in her Yorkshire constituency during the European Union referendum campaign.
Leadbeater, who represents the same Batley and Spen seat, told the BBC programme: "I think politics was in a pretty bad place at that time. There was a lot of division. There was a lot of anger."
"Sadly, I would say, if anything, it's worse."
She added: "Elected officials not feeling they can always speak freely, not feeling they can always say what they really think."
"And potentially, worst case scenario, not necessarily voting in the way that they think they should vote because they know the impact it's going to have on their safety, but also on their mental health and well-being.
"And that is a really dangerous place to be. That is not good for democracy."
Earlier this year, Prime Minister Rishi Sunak warned the UK could be descending into "mob rule" amid fears about MPs being targeted by demonstrators over the Israel-Hamas conflict.
Meanwhile, Colburn, who has spoken in the Commons about a 2021 suicide attempt, told the programme: "Colleagues from all UK political parties have attempted to take their own life."
The programme had exclusive access to preliminary findings of a 2024 survey of departing MPs, highlighting the impact of the job on their mental health.
It also includes new evidence from the House of Commons, which suggested that mental health is one of the most common reasons those in Westminster contact its medical services.
Matt Hawkins, co-director of the campaign group Compassion in Politics, said: "We need to have a national conversation about the harm our political system is doing to anyone who seeks to work in it or with it."
"Toxic debates, abuse, long hours, lack of autonomy – these are just some of the issues that are taking a massive toll on our elected representatives and their teams."
"But the problem doesn't stop there. These are the individuals being chosen to represent our interests, and they are having to do so while perennially exhausted, often anxious, and sometimes depressed."
"If we want to change our country for the better, we need to change our politics and help create a political environment that is inclusive, welcoming, supportive, and caring."