Council leaders have demanded urgent measures to tackle what they say is a tide of abuse against councillors, potentially including a specific law against intimidating public officials and a greater willingness to prosecute those who make threats.

A meeting of senior local government leaders from across England heard of regular death threats against councillors and routine abuse or accusations of corruption on social media and in comments under local newspaper website stories.

The executive advisory board of the Local Government Association (LGA), which groups together several dozen council leaders from various parties, had already begun gathering information about the issue before the killing of the Conservative MP Sir David Amess last week.

But in a meeting on Thursday, a series of councillors recounted receiving death threats, saying that the extent of intimidation risked seeing many people put off from putting themselves up for election.

“You shouldn’t have to be a brave superhero to want to stand and represent your community,” said Tudor Evans, the leader of the opposition on Plymouth council, who said he had once been sent a death threat because of a temporary traffic light scheme.

Evans recounted how the previous week in Plymouth, a man had gone into a cafe with a knife in his belt and made threats against local councillors.

Nick Forbes, the leader of Newcastle council, said he had quit almost all social media due to a “daily background” of messages containing homophobic comments or accusations of corruption.

Forbes said he and colleagues felt things were so bad that ministers needed to act. “In the same way that there is additional protection for, for example, police officers and NHS staff, we thought that there should be a specific offence of intimidating or harassing a public official,” he said.

Forbes said the police response to even direct threats was “patchy”, and called for officers and prosecutors to adopt a “zero tolerance approach to harassment”.

While saying that councillors had to make sure their discourse was “mature and sensible”, Forbes argued that some local papers played a role in fomenting hatred: “We need the media to take a responsible attitude, to not boiling complicated, complex issues down to good or bad, demons or heroes, providing clickbait and often using the language of aggression.”

Georgia Gould, the leader of Camden council in north London, said the extent of intimidation was such that councillors should be able to opt out of having their home address publicly visible. She said: “Most of us have probably received some kind of death threat, or other difficult visits to our homes, and I just don’t think it’s a safe situation.”

Isobel Seccombe, the leader of Warwickshire county council, who heads the LGA’s Conservative grouping, said she too had received threats, but was worried that it was becoming so routine that it was seen as inescapable.

She said: “That’s the problem, that we do accept this as a consequence of being a councillor. And our acceptance of it is, in a way, contributing to the problem.”