MPs have warned that Brexit has coarsened public debate to the point where they regularly receive death threats and other forms of intimidation via social media and elsewhere, with many using panic buttons for their own safety.

One MP, who asked not to be named, said she still received “death threats every single day” despite heightened security measures. They were stepped up after the murder of the Labour backbencher Jo Cox in the run-up to the 2016 EU referendum.

Rupa Huq, the Labour MP for Ealing Central and Acton, said she had received an email over the weekend suggesting that she “return to Bangladesh to ponder your life if you do not come to your senses over Brexit shortly”.

After calling Huq “a miserable, stinking, filthy EU whore”, the anonymous author told the MP: “You should abandon your new referendum anti-democratic rhetoric and either vote for the government deal or not obstruct a no-deal exit.”

The MP tweeted out the message and got many comments of support. She said she believed that “Brexit has done this to us – with the help of social and other electronic media” making it much easier for the public to abuse elected representatives.

Staff working for MPs often have to bear the brunt of abuse as they deal with correspondence. “Twenty years ago, they had to deal mostly with stationery and filing cabinets, but now people have to deal with whatever comes into the office every day,” Huq said.

All MPs are offered panic buttons – which connect to police control rooms – to install at home and carry around on their person. The devices cost nearly £1,000 a year.

Huq was talking a day after the shadow education secretary, Angela Rayner, said she had received rape and death threats from “someone claiming to be a Jeremy Corbyn supporter” and further abuse via social media after she had praised Tony Blair’s performance in a TV interview.

Rayner’s comments struck a chord with many of the party’s MPs at a time when tensions within Labour are high over concerns about antisemitism and other forms of bullying. She also said she had panic buttons fitted at home.

Some MPs believe that politicians have to play a role by cooling down their rhetoric. Paula Sherriff, the Labour MP for Dewsbury, said: “We’ve got to find a way of getting the temperature down.”

She cited, as an example, the tone struck by Michael Gove in his attack on Corbyn at the end of January’s no-confidence debate when he claimed the Labour leader “won’t stand up against Putin when he attacks people in this country”.

But MPs from all parties have voiced concern about their safety, particularly in the run-up to next week’s key Brexit votes.

Nicky Morgan, a former Conservative minister, told the Commons on Monday evening that she feared MPs were on the receiving end of “systematic intimidation” in an attempt to force them to change votes on Brexit.

She asked John Bercow whether “this threat to our democracy and to our safety is to be taken seriously and challenged at all times”, prompting the Speaker to reply that “women are disproportionately targeted” and that “this is intolerable”.

Anna Soubry, who recently defected from the Conservatives, was repeatedly targeted by abusive far-right demonstrators as she went to television interviews outside parliament, prompting a security review that has led to more interviews being conducted inside the building.

Alison McGovern, a Labour backbencher, said she would advise anyone newly elected to parliament to keep an eye on their safety and avoid seeking out abusive comments on social media aimed at them. “People coming into politics need to ensure they have enough blinkers on to survive,” she said.