A Labour MP has called on party leader Jeremy Corbyn to “name and shame” social media trolls after revealing that she has received 25,000 abusive messages over the past few months alone.

Counter-terrorism police have launched an investigation into an anti-Semitic death threat received by Ruth Smeeth, which allegedly called for the Stoke-on-Trent North MP to be hung from the gallows.

While accepting that the messages were not being initiated by Mr Corbyn, Ms Smeeth said that they were being sent “in his name” and she held him “personally responsible” for them.

She said Jewish and female MPs like herself were “bearing the brunt” and insisted it was not enough for the Labour leader simply to condemn abusive behaviour.

“It’s vile, it’s disgusting and it’s done in the name of the leader of the Labour Party, which makes it even worse,” Ms Smeeth told BBC2’s Victoria Derbyshire programme. “I know that Jeremy Corbyn would condemn this, but it’s not about condemning, it’s about what people are doing in his name.

“What I need is for the leader of my party, the leader of Her Majesty’s opposition, to make it clear what can be done. He should be naming and shaming some of the worst perpetrators who are doing it in his name, and making it clear publicly that they do not speak for him, that this is unacceptable.

“There is a vile amount of racism and intolerance and abuse online, which then feeds on to our streets and leads to a culture of intolerance that he could actually personally do something about. That’s what I’m asking him to do.”

A spokesman for Mr Corbyn said: “Jeremy has consistently spoken out against all forms of anti-Semitism and has contacted Ruth Smeeth to express his outrage at the abuse and threats directed against her.

“Jeremy condemns all abuse, and no one responsible for it is a genuine supporter of Jeremy’s. He has repeatedly called for a kinder, gentler politics.

“This is why he launched Respect and Unity, a code of conduct calling on all Labour members and supporters to conduct themselves with a high standard of behaviour. Evidence of threats and abuse should be reported to the party and police so that action may be taken against those responsible.”

Corbyn’s leadership rival Owen Smith said: “Anti-semitic abuse and violent threats against Ruth Smeeth, or anyone else, are completely unacceptable. I condemn them unreservedly and Ruth has my full support.

“Anyone responsible for abuse like this has no place in the Labour Party. There can be no excuses for abuse, and it should never be ignored.”

The flood of abusive messages began in June, shortly after Ms Smeeth fled the launch of Labour’s report into anti-Semitism in tears after being accused by an activist of colluding with the right-wing press.

She later accused Mr Corbyn of a “catastrophic failure of leadership” for failing to intervene during the incident, and said the Labour Party “cannot be a safe space” for British Jews.

Ms Smeeth said: “Since the end of June I’ve received somewhere in the region of 25,000 pieces of abuse. I got 20,000 pieces of abuse within 12 hours, and once it starts on social media it keeps going.

“Most of it was on social media, most of it on Twitter, a great deal on Facebook, and then calls to my office and emails.”

One message referred to police branded the MP a “dyke” and a “CIA agent”. The message accuses her of “treason” and says the gallows would be a “fine and fitting place” for her.

Ms Smeeth told The Sun: “What concerns me most is the impact it has on my staff, who see it before me.

“But I am quite clear that I will not be intimidated by any of these people. I was elected to serve my constituents and I have a job to do.”

The Metropolitan Police confirmed that its Counter-Terrorism Command was conducting an investigation into allegations of malicious communication and threats to kill made via social media.

“That investigation is ongoing,” said a spokesman. “At this stage, whilst there have been no arrests, a number of lines of inquiry are being actively pursued.”

A Labour spokeswoman said: “The Labour Party fully supports the work of the police in ensuring the safety and protection of all MPs and their staff.

“Threatening behaviour will not be tolerated within the party and we urge anyone receiving any abuse to contact the party and, where relevant, the police.”

Board of Deputies Vice President Marie van der Zyl called on Labour’s leadership contenders to condemn online anti-Semitism, adding that the incident shows “the depths which some so-called Labour supporters are plumbing.”

“This needs to be roundly and swiftly condemned by both the leadership candidates and the Party needs to act to drain the cesspit of anti-Semitism that has become so apparent in recent months.

“This will not happen if leading Labour figures continue to irresponsibly undermine the disciplinary process that has, often belatedly, led to the suspension of bigots. Casting doubt on the actions that are being taken means that certain Labour figures are effectively giving a ‘free pass’ to racism and misogyny and creating a culture of impunity for antisemitism.”

“Labour’s disciplinary process needs to be strengthened, not undermined.”

Simon Johnson, CEO of the Jewish Leadership Council added: “The threats targeted at Ruth Smeeth MP have no place in society. The Leader of the Labour Party seems to have no control over his ‘so-called’ supporters and his repeated condemnations have not begun to tackle antisemitism within his party.  Where individuals are known to Mr Corbyn, he must act to protect his MPs. His calls for a ‘kinder, gentler politics,’ are proving to be at best a cover-up for his lack of decisive action and at worse something far more sinister.”