Experts have urged caution in the face of pressure on internet companies to remove extremist websites and calls by MPs and others for a clampdown on the dissemination of online jihadist rhetoric.

The home secretary, Theresa May, said on Sunday she wanted to see what more could be done to police online messages preaching violence or jihad, adding: "One of the issues we need to look at is whether we have got the right processes, the right rules in place in relation to what is being beamed into people's homes."

However, Tim Stevens, co-author of a major piece of research in 2009 into countering online radicalisation, warned that little had changed since the report, which concluded that any strategy that relied on reducing the availability of online content alone was bound to be crude, expensive and counterproductive.

He added that the calls for the revival of the communications data bill, "a law enforcement, intelligence gathering measure", were being conflated in the wake of the killing of Drummer Lee Rigby with "an idea that somehow taking down internet sites and so on is a way of countering radicalisation".

"Anyone who knows anything about the internet knows that just [even if] you take something off the internet, [it] is likely to be back on it again within an hour, or downloaded on to hard drives," said Stevens, an associate fellow of the International Centre for the Study of Radicalisation.

He added: "My feeling is that the police have got better things to do, and so do the intelligence services, who already have the tools and powers to see who is seeing material, downloading it and putting it up.

"The police are in a different position because when they see it they are supposed to do something about it. I suspect they turn a blind eye much of the time because they have got some criminals to catch. With an issue like this, poor legislation can be worse than no legislation."

Jamie Bartlett, the director of the Centre for the Analysis of Social Media at Demos, added: "One of the big problems is that a lot of the material which is used to radicalise people – and many observers have a problem with that term – or used to get some form of motivation and justification, is actually legal."

"It is sermons of a religious nature on YouTube that do not call people to act. It is videos of massacres in the Muslim world which are on BBC as well as everywhere else. So there is always a big problem with trying to crack down. The other problem is playing catch up, taking material down which pops up again somewhere else."

Speaking on Sunday on the BBC, May said: "There has been discussion of a greater use of court orders to block some sites, but it will be difficult to decide whether responsibility will lie with the Home Office or internet service providers."

Google has said that it relies on the public to flag up incendiary material.

YouTube said videos of a "purely religious nature" would remain online.