Boris Johnson is facing calls to enact “David’s law” to crack down on social media abuse of public figures and end online anonymity in the wake of the killing of Sir David Amess.

Dozens of MPs paid tribute in the House of Commons on Monday to the veteran Conservative backbencher who was stabbed to death on Friday, shedding tears, sharing uproarious anecdotes and venting anger over his death.

While police are investigating whether there are any links to Islamist extremism and have not connected the killing to the targeting of MPs online, allies of Amess said he had voiced growing concern about threats and toxicity within public discourse as they demanded a crackdown.

Campaigners have warned, however, that ending online anonymity could put whistleblowers and pro-democracy campaigners in authoritarian regimes at risk. Keir Starmer, the Labour leader, told the Commons that “civility in politics matters” but “we must not lose sight of the fact that David’s killing was an [alleged] act of terror on the streets of our country”.

Mark Francois, who described Amess as one of his closest friends and his political mentor, vowed he would dedicate his time in parliament to overhauling the rules governing social media.

Francois told the Commons he was “minded to drag Mark Zuckerberg [CEO of Facebook] and Jack Dorsey [CEO of Twitter] to the bar of the house … if necessary kicking and screaming so they can look us all in the eye and account for their actions or rather their inactions that make them even richer than they already are”.

He said MPs should radically toughen up the pending online harms bill to prevent trolls and other abusers hiding behind pseudonyms. “In the last few years David had become increasingly concerned about what he called the toxic environment in which MPs, particularly female MPs, were having to operate in,” Francois said.

“He was appalled by what he called the vile misogynistic abuse which female MPs had to endure online and he told me very recently that he wanted something done about it.”

Francois, the MP for Rayleigh and Wickford, which neighbours Amess’s Southend West constituency, added: “I suggest that if we want to ensure that our colleague didn’t die in vain, we collectively all of us pick up the baton, regardless of our party and take the forthcoming online harms bill and toughen it up markedly.

“Let’s put, if I may be so presumptuous, David’s law on to the statute book, the essence of which would be that while people in public life must remain open to legitimate criticism, they can no longer be vilified or their families subject to the most horrendous abuse, especially from people who hide behind a cloak of anonymity with the connivance of the social media companies for profit.”

Bernard Jenkin said MPs should also examine themselves when discussing civility in politics, a nod to some of the disturbing language used during Brexit debates. “Which of us has never felt fallen prey to feelings of contempt or lack of respect or unkindness towards those who oppose us? Which of us can honestly say we cannot do better?” He said kindness should be added to the seven principles of public life. “Henceforth, let kindness be known as the David Amess principle of public life.”

Amess, an MP for 38 of his 69 years, was stabbed to death while holding his constituency surgery in an Essex church. Ali Harbi Ali, 25, was arrested at the scene and continues to be detained under terrorism laws.

The government intends to pass an online safety bill introducing new obligations on social media companies to regulate illegal and harmful material – though there has been significant controversy over how that can be defined. Compliance will be monitored by Ofcom and the bill is expected to start its passage after pre-legislative scrutiny set to report back in early December.

Paying tribute to “one of the nicest, kindest and most gentle individuals ever to grace these benches”, Johnson said Amess’s killing struck at the heart of the ordinary democratic work of MPs. “That Sir David spent almost 40 years in this house but not one day in ministerial office tells everything about where his priorities lay,” he said.

“He was not a man in awe of this chamber, nor a man who sought patronage or advancement. He simply wanted to serve the people of Essex, first in Basildon, then in Southend. And it was in the act of serving his constituents that he was so cruelly killed.”

Starmer said: “Even as a political opponent he was a man and a politician we could all learn much from. I use that phrase – ‘political opponent’ – very deliberately. Because David held his beliefs passionately but gently. I believe that not only can we learn from that but that we have a duty to do so. Civility in politics matters.”

Starmer spoke to the parents of Jo Cox, the Labour MP murdered by a far-right terrorist in 2016, on Friday, he said. “I knew they would be reliving that terrible day. They said to me they were thinking of David’s family and how their lives would be changed forever,” he said.

Cox’s widower, Brendan Cox, also said it was a moment to reflect on political discourse and a “day-to-day brutality with which our political debate is conducted, from increasingly regular death threats to online abuse”. The police team convened after his wife’s murder to investigate threats against MPs found 582 reports of malicious communications and handled 46 cases of harassment between 2016 and 2020, he said. Nine cases were classified as terrorism-related.