Female MPs should receive training to deal with vicious online trolling, Labour’s Tulip Siddiq has said, revealing several MPs who are frequent targets of abuse have formed their own unofficial support group in the House of Commons.

“We meet online and in the tea rooms. We support each other as MPs and as women,” the Hampstead and Kilburn MP told the Sunday Times. “Online abuse can be really frightening and upsetting for some women.”

Siddiq said she had been targeted from all sides of the political debate, including receiving death threats and criticism for having her baby daughter while she was in her first term in parliament.

“I have had horrendous abuse... ranging from, ‘Why aren’t you wearing a hijab?’ to ‘If I could I would kill you’.

“Women – or their Twitter profiles said they were women – said things like, ‘Make up your mind, you are either a mother or an MP, you can’t do both’.”

Siddiq said she believed the online abuse is a direct response to a new generation of strong-minded and opinionated women in the House of Commons. “They do not feel they have to shut up,” she said. “For some people that’s a big change – they are not used to handling women like that.”

Several high-profile Labour MPs, including Jess Phillips and Stella Creasy, as well as the former shadow home secretary Yvette Cooper, have warned that online abuse is stifling political debate.

Phillips, the MP for Birmingham Yardley, said last week she was considering leaving Twitter after receiving a wave of abuse for calling out a tweet that said: “I wouldn’t even rape you.”

“I could never block them,” Phillips told the BBC’s Victoria Derbyshire programme. “You would need someone employed full time to block the amount of people who have been in touch with me over the weekend.

“It’s not a solution just to block and ignore them in my case. The only solution in stopping me seeing it is if I stop going on Twitter, which is a very real possibility.”

Cooper has called for online threats, harassment and stalking to be included in the Crime Survey for England and Wales, as part of a cross-party campaign called Reclaim the Internet, modelled on the Reclaim the Night campaign for safer streets from the 1970s.

“We need to do the same again now so women are not silenced on the new streets of social media, so no one is drowned out by bullying and abuse,” she wrote in an article for the Guardian.