Conservative MP Louise Mensch has claimed she has received threats against her children from the hacking groups Anonymous and LulzSec.

The MP for Corby made the claim on Twitter in the early hours of Monday morning from New York, where she is spending her summer holiday, but did not reveal the nature of the threat she had allegedly received.

She tweeted: "Had some morons from Anonymous/Lulzsec threaten my children via email. As I'm in the States, be good …to have somebody from the UK police advise me where I should forward the email."

She said she was revealing the information on Twitter because the threat aimed to warn her off using the social media network.

She later added that she had reported the incident to the police in the House of Commons. The Commons authorities are referring queries to Scotland Yard, which said it was aware of the allegations and was looking into it.

Mensch, who wrote popular fiction before entering the Commons last year, is an avid user of Twitter and has embarked on a number of high-profile debates in recent days about social media blackouts during the recent riots, phone hacking and Sally Bercow's appearance in the Big Brother house.

LulzSec – Lulz Security – and Anonymous are hacking groups that advocate civil disobedience on the internet. LulzSec was behind the hacking of News International websites at the height of the News of the World phone-hacking revelations and a separate operation against Nintendo.

A hoax story posted on the Sun website suggested Rupert Murdoch had been found dead after having taken the rare-earth metal "palladium" before "stumbling into his famous topiary garden late last night". The page later redirected to LulzSec's Twitter account.

Anonymous has targeted the Church of Scientology, Visa and Mastercard, and various Middle Eastern governments in the pursuit of what it sees as transparency and individual liberty.

In a statement, Mensch said: "Having discussed the matter with House of Commons police, and on their advice, I will not be releasing the email as they investigate; I do intend to release it once the police investigation has finally concluded.

"I am extremely grateful for the prompt action of police in parliament and in Northamptonshire in securing my family and in working hard to trace who sent these cowardly threats."

A spokesman for the Metropolitan police confirmed that they had received an email making a complaint about malicious communications.