A Conservative MP who last week rebelled over Brexit has submitted a dossier of threats of violence against her to the Speaker as Theresa May and Jeremy Corbyn condemned an increase in intimidation against MPs.

A document provided by Anna Soubry and seen by the Guardian includes dozens of examples of threats, including several calls for her to be hanged for treason. The messages have been received since she was called a “mutineer” on the front page of the Daily Telegraph alongside colleagues and then, last week, voted against the government.

Dominic Grieve, who led last week’s push for MPs to be given a “meaningful vote” on the final Brexit deal, also reported death threats to the police, while another MP told the Guardian they had been forced to use a panic alarm in their constituency office.

May used a statement to update parliament on last week’s EU council meeting in Brussels to address the question of intimidation.

“We are dealing with questions of great significance to our country’s future – so it is natural that there are strongly held views on all sides of this chamber, and it is right and proper that we should debate them and do so with all the passion and conviction that makes our democracy what it is,” the prime minister said.

“But there can never be a place for the threats of violence and intimidation against some members that we have seen in recent days – our politics must be better than that.”

Corbyn highlighted a newspaper front page that accused the 11 Tory rebels of being a group of “self-consumed malcontents” and asked: “Proud of yourselves?”

“The Daily Mail, which previously branded members of the judiciary as enemies of the people, is now whipping up hatred against backbench rebel MPs,” the Labour leader said. “Threats and intimidation have no place in our politics.”

May said it was a “bit rich” for Corbyn to intervene, given the abuse of Tory MPs during the election. But the Labour MP for Dewsbury, Paula Sherriff, said this was not a partisan issue.

The dossier provided by Soubry is divided into the response she received after the Telegraph accused her and colleagues of being mutineers and those received after she and others voted against the government on amendment 7.

In one message, an individual said they would love to go on a tour of Westminster “but can’t make enough explosives in time”. Another asked whether Soubry should be subject to treason charges along with May, Amber Rudd, the home secretary, and Philip Hammond, the chancellor. “Is there enough rope to hang them along the Embankment?”

Others described MPs as “scum”, called for deselections and for them to be hanged, drawn and quartered, while one used a hashtag naming the Labour MP Jo Cox, who was murdered by a far-right extremist. It said the “mutineers” had committed treason and their “heads belong on spikes outside”.

Soubry made clear she wanted to show the Speaker, John Bercow, the scale of the intimidation.

“We’re in danger of fanatical ideologically driven extremists controlling British politics,” she said, claiming that hard-right Brexiters and supporters of the leftwing group Momentum were using “bully-boy tactics”.

“The internet provides the means for these extremists to peddle their hatred and paranoia. But party leaders must call them out and condemn them,” Soubry told the Guardian, also highlighting media coverage.

“Certain sections of our media must understand the responsibility they have to report accurately and in a way that doesn’t fuel intolerance and prejudice. And all of us in politics, Labour and Conservative, must speak out against this tyranny. Our democracy is seriously under threat and we must stand up and defend it.”

In response the Speaker of the Commons told MPs: “As members of parliament, you are never traitors, you are never mutineers, never malcontents, never enemies of the people.”

The Labour MP Chris Bryant said that since the 14th century, the Speaker of the Commons had demanded freedoms for MPs, including to “speak freely without fear or favour”.

He highlighted a case in 1957 when a newspaper editor, John Junor, was brought before the bar of the House of Commons after condemning a government scheme that gave politicians generous petrol allocations. He was found in contempt of parliament because of fears of the backlash that MPs would face.

“Everyone felt it was an attempt to threaten and intimidate the politicians,” said Bryant, who argued that intimidation was now common practice across a range of subjects that stretched beyond Brexit.

He said it was critical for politicians not to support threats from individuals or newspapers.

“Stop retweeting and deselections. Let us treat each other with respect. It is dangerous to a democracy – who wants to be an MP in a world in which you just take endless abuse, what does it do to the mental health of MPs?”

The Labour MP Stephen Doughty later outlined other examples of intimidation. “I too have had the threats. I’ve had a fake bomb sent to my office, the homophobia, the threats of hanging, a threat this week that all traitors should be shot.”

“There is a plague on all our houses in the way that the fringes of political parties operate. I am sick and tired of the abuse – I had a local party member post that hanging was too good for me.”A Tory MP said: “We are tolerating violence of language and it is being fuelled by sections of the press. The frenzy unhinges everyone a bit, but completely unhinges the already very unhinged. And that is how you get violent acts as we saw with Jo Cox’s murder.”