Detectives carrying out the multimillion-pound investigation into illegal newsgathering techniques at Rupert Murdoch's British newspaper group have been asked to investigate whether it attempted to blackmail politicians.

The alleged plot centres on News International's apparent efforts to warn off MPs on a parliamentary committee from disproving its discredited defence that phone hacking was the work of a single "rogue reporter".

According to the former senior News of the World journalist Neville Thurlbeck, News International ordered the Sunday paper's reporters to scour the private lives of MPs on the Commons Culture, Media and Sport Committee in 2009. At the time, Mr Murdoch's company was mounting what it now admits was a mistakenly "aggressive" response to allegations that the interception of voicemail messages was rife at its headquarters in Wapping, east London. On the advice of the parliamentary authorities, the Labour MP Tom Watson has now asked the Metropolitan Police to investigate the allegation.

According to Mr Thurlbeck, reporters were told by those in "deepcarpetland" to obtain evidence of affairs or gay relationships. The aim, he claimed, was to "to find as much embarrassing sleaze on as many members as possible in order to blackmail them into backing off from its highly forensic inquiry into phone hacking". In a letter – a copy of which has been obtained by The Independent – to the Deputy Assistant Commissioner leading the Met's inquiries into News International, Sue Akers, Mr Watson wrote: "If these allegations are found to be true, it suggests there was a conspiracy to blackmail."

Mr Watson, a member of the committee put under surveillance by News International, said: "I have evidence that I was put under covert surveillance in September 2009 by the private investigator Derek Webb, as well as Mazher Mahmood and an accomplice. Mr Thurlbeck may not be aware of this. I would, therefore, urge you to investigate Mr Thurlbeck's claims in order to establish whether any offence was committed."

The Met launched an inquiry into alleged computer hacking at The Times earlier this year in response to a letter from Mr Watson. Yesterday the Met said it was unable to comment on the MP's latest request. The Leveson Inquiry – where former Labour Prime Minister Tony Blair will appear today – has been investigating the power wielded behind the scenes by News International. While blackmail would be a significant deepening of the criminal inquiries enveloping NI, former News of the World reporters have spoken in the past about their use of "leverage" to secure the co-operation of people about whom the paper had embarrassing information.

Mr Thurlbeck, the former chief reporter, disclosed the alleged operation against MPs in comments to Mr Watson that the MP included in his co-authored book, Dial M for Murdoch. Mr Thurlbeck said that an "edict" had been passed to reporters to "find out every single thing you can about every single [committee] member: who was gay, who had affairs, anything we can use."

In the New Statesman this month, he added that the NOTW's journalists had been so concerned about the exercise that they did not carry it out, but went further than he had previously about its intent. He wrote: "At the height of the hacking scandal, News of the World reporters were dispatched round the clock... the objective was to find as much embarrassing sleaze on as many members as possible in order to blackmail them into backing off from its highly forensic inquiry into phone hacking."

In his letter to Ms Akers, dated 9 May, Mr Watson wrote: "I think it is important that I write to make you aware of new information published by Neville Thurlbeck.... The comments concern the blackmail of members of the Culture, Media and Sport Select Committee, and will be of interest to you given Mr Thurlbeck's previous arrests."