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The former global counter-terrorism director of MI6 has said it would be impractical and unfair to expect Facebook to monitor messages for terrorist intent and report them to the security services.

The social media site, and other internet companies, are facing demands to police their content on behalf of the state after an official report into the death of Lee Rigby said that one of his killers wrote on a website - later named as Facebook - of his desire to slaughter a soldier, without the security services knowing.

Richard Barrett, a former counter-terrorism chief at MI5 and MI6, said that he doubted the capacity of Facebook to sift through the volume of content handled by the website each day, as well as that of the security services to deal with the amount of information that would be referred to them if an obligation was placed on internet companies.

'Facebook has about one and a third billion users and about five billion posts a day so clearly on a worldwide basis it would be almost impossible to deal with the amount of stuff that was referred,' he told BBC Radio 4's Today programme.

'And even in the United Kingdom there are about 25 million users of Facebook and so let's say possibly about 125m posts a day. And even if you take out all the pictures of kittens which were put up you'd still be left with an awful lot to go through and then quite a percentage of those perhaps would be passed on for the police or security services to look at. So it would be an enormous task, I think.'

A report published on Tuesday by the parliamentary intelligence and security committee (ISC) said the authorities were never told that one of the killers, Michael Adebowale, wrote of his murderous intent six months before he and his accomplice, Michael Adebolajo, brutally attacked Rigby in May 2013 in a street near his military barracks and attempted to behead him. In the wake of the ISC report, David Cameron said it was companies' social responsibility to report when their networks were being used 'to plot murder and mayhem' and vowed action.

But Barrett said: 'I think it's very hard to talk about the social responsibility of a multinational company. I mean Facebook is operating in probably almost all countries in the world, so will that social responsibility vary do you think from the United Kingdom to, I don't know, Russia or Myanmar or countries like that? I think it's quite a burden to put on Facebook to decide where their social responsibility lies in all different circumstances.'

He said that eight social media accounts run by Adebowale had been closed down because they had been flagged as promoting terrorism by an algorithm that did not require human input. Asked whether the authorities should have been told about the posts, he said: 'It's unfair to ask the companies to make that decision. I think there has to be a proper legal basis so they know what they are to do and what they don't need to do.'

But he made clear that he was unconvinced by the value of such legislation, questioning what value it would have in light of the sheer amount of questionable material that would be referred.

He added that people who wanted to get around restrictions placed on their communications could probably do so quite easily by using encryption.