The Labour MP Jess Phillips was bombarded with more than 600 rape threats in a single night, she has revealed, as she called for online trolls to no longer be allowed anonymity.

Phillips said she is constantly the object of vicious abuse online, with the police having issued harassment orders against two people. She has concluded from her experience that parliament needs to force people to make their identities available to the likes of Facebook and Twitter – even if they are still able to remain anonymous to the general public.

“In one night, I received 600 rape threats. It was probably more but I stopped counting. To try to subvert that, I received thousands of comments from people saying ‘I wouldn’t even rape her’,” the Birmingham Yardley MP told the Cheltenham Science Festival.

She said that, to her, it was “water off a duck’s back” because she does not consider herself or her children to be in physical danger. “However, where it does worry me, and I think we have to do something about, is when it affects our democracy.

“I don’t think people should be allowed to be completely anonymous online any more. I don’t mind if people appear anonymous online for all sorts of really reasonable reasons.”

Phillips cited the example of a teacher in her constituency who wanted to speak out against government cuts in schools. “They want to be anonymous, but they wouldn’t mind not being anonymous to the provider and tell Facebook or Twitter who they are. But, to the public, they want to appear anonymous.

“Anyone who wishes to damage our democracy can just write all that stuff. I think we have got to try to do something about this and I think the anonymity debate is probably where parliament will lead.”

Over the weekend the security minister, Ben Wallace, said digital IDs should be brought in to end online anonymity that permits bullying and grooming. During the G7 summit the prime minister, Theresa May, called for the tech giants to clamp down on attacks against women.

Phillips said the number of threats directed at her “has its peaks and troughs depending on what I’m talking about”. She said: “If you speak from a feminist perspective, which I very frequently do, you will suffer from a huge amount of internet trolling, largely from what seems to be the “alt-right”.

“The other sort of trolling MPs suffer is issue-based or ideologically based, whether you agree with Jeremy Corbyn or not, which is a classic reason to be trolled mercilessly.”