A Conservative-backed plan to allow police and the security services unprecedented access to people’s internet communications would not have helped prevent the murder of Lee Rigby, M15 officers have indicated.

Senior security sources have told The Independent that attempts to cite last Wednesday’s killing as a reason to push forward with the controversial “snooper’s charter” was a “cheap argument”.

The remarks will be seen as a rebuke to the Home Secretary, Theresa May, who suggested at the weekend that the Draft Communications Bill was “essential for the intelligence agencies” to combat the threat of terrorism.

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In fact, the security source suggested, the Bill would be of greater use to the police in gathering evidence in the early stages of an investigation than it would be in preventing the type of attack seen in Woolwich.

They stressed any decision to proceed with the Bill, which is being blocked by the Liberal Democrats, was a political one and the effect on civil liberties would have to be taken into consideration.

Today, it also emerged that the head of MI5, Andrew Parker, has written to the Parliamentary Intelligence and Security Committee setting out what the security services knew about the activities of the Woolwich suspects Michael Adebowale and Michael Adebolajo. This follows talks between Mr Parker and Sir Malcolm Rifkind, the chairman of the committee, last week.

In the wake of the attack it emerged that Adebolajo and Adebowale were both known to MI5 – and may have been approached to act as informers.

Today, Adebowale was taken to a police station in south London after being released from hospital.

He was formally arrested on suspicion of the murder and suspicion of the attempted murder of a police officer.

He will now be interviewed by detectives from the Metropolitan Police Service Counter Terrorism Command.

In an interview, Sir Malcolm insisted that MI5 was not being criticised over the killings. “I don’t think they’re in the dock. I think that would be very unfair,” he said.

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“Do remember one fundamental point: the fact we have not had anyone killed until these tragic events in Woolwich since the 7/7 bombings [in London] in 2005 is not because there hasn’t been terrorist plots. Every year since 2005 there has been at least one, sometimes two or even more, terrorist plots which were disrupted and prevented from killing British citizens, partly because of the work of MI5 – in some cases very largely because of the work of MI5 – and other intelligence agencies.”

Sir Malcolm said he was very confident the committee would get to the bottom of MI5’s work related to the Woolwich incident and that Mr Parker had offered him assurances that MI5 would fully co-operate with the investigation. The ISC has Parliament-approved powers to access all relevant files and internal papers from MI5.

Sir Malcolm said that after the ISC deliberations, David Cameron and Parliament would receive a report.

He added that elements of Parliament’s report might be redacted for public viewing on the grounds of national security.

Sir Malcolm added that the effect of government spending cuts on the security services would also be analysed during the ISC’s review.

“We would be concerned if there were to be any further reduction in resources for the intelligence agencies,” he said.

“Whether this is relevant to the Woolwich incident, frankly I’m not going to comment on it at the moment. We will go where the evidence takes us and we will come to a judgement as to whether that is indeed part of the problem, if there was a problem or if it’s not relevant to this particular matter.”