Rival politicians Matt Hancock and Rupa Huq have united to urge that Sir David Amess’s murder sparks permanent change to tackle online hatred of politicians and “set public debate on a better path”.

In a co-authored column in The Times, Tory Mr Hancock and Labour’s Ms Huq said the killing of the veteran MP had “shocked parliament to its core”, and that they had also been “disgusted” to see MP Michael Gove harassed in public only days later.

The pair said democracy “cannot survive a continuing coarsening of public debate” and called on social media companies – “the creators of algorithms that feed people content that only reinforces what they already think” – to bear responsibility.

They also shone a light on the difficulty of enforcing libel laws in the internet age.

“There have been hecklers as long as there have been public meetings. But using online social media, keyboard warriors post accusatory, aggressive messages often based on conspiracy theories and lies. Our timelines and inboxes are awash with threats,” Mr Hancock and Ms Huq wrote.

They pair said female politicians, particularly from ethnic minority backgrounds, received the worst online abuse but white men were not immune, citing one social media post calling for Mr Hancock to be executed live on BBC One.

The murder of MP Jo Cox, they wrote, had been followed only weeks later by “unprecedented vitriol” surrounding the EU referendum.

“This time we must make permanent changes to tackle the problem and set public debate on a better path,” they said. “The online harms bill is a good start, but it does not yet tackle anonymous abuse.

“It is a particular problem that libel laws don’t work in the internet age. It is hard to prove that a single post by a social media user with a few hundred followers causes significant damage, but when that post is shared and added to by hundreds or thousands of others, it has the same effect as a defamatory newspaper piece in days gone by.”

Saying politicians also needed to treat each other with respect, Mr Hancock and Ms Huq said threats could no longer be ignored and that a permanent campaign was needed “because ‘keep calm and carry on’ is no longer an option”.