David Cameron was on fighting form in the House of Commons last week. He was outlining to MPs the government's plans for the coming year, as summarised in the Queen's Speech. He was especially bullish and uncompromising when it came to the issue of tackling 'non-violent extremism'. Tim Farron, the leader of the Liberal Democrats, quoted the Prime Minister's own reviewer of terrorist legislation, David Anderson, who has warned that the government's plans risk "playing into the hands of those who, by peddling a grievance agenda, seek to drive people further towards extremism and terrorism" – a pretty serious accusation.

The Prime Minister's response was strongly worded: "our liberal values in this country" – freedom of speech, equality, democracy, etc – "are being stamped out all over by people saying, '[as a woman] you can't travel out of the city you live in', or, 'you can't mix Jews and Muslims'... we have got to stand up and fight for liberal values." And to those who say that it is dangerous for the government to move beyond criminalising violence hate speech, and start criminalising 'non-violent extremist' ideas, teaching and beliefs, he was equally firm: "It is no good saying, as the Liberal Democrats sometimes do, 'Let's just focus on the violent extremists; everyone else is just exercising their freedom of speech.' That is not good enough in a liberal democracy."

The problem facing David Cameron is that it is not just the Lib Dems who are saying this. Experts from across society are saying similar things.

Obviously, there is agreement that there are practices going on in the UK which are not violent but are extremist, which must be addressed. In his speech, Cameron mentioned "the so-called community leaders who say women cannot travel more than a few miles beyond the city in which they live; the activists who insist on segregation at political meetings; and the religious schools that teach children not to mix with those from different religions, and that sometimes teach that Jews are the enemy." Clearly, these are all troubling practices which repress people, and which will create wider social problems if allowed to go unchallenged.

The issue Cameron faces is not a lack of willingness to tackle these problems; it is the serious and often scathing criticism of his solutions from a wide range of experts – some of whom even say his plans will make the situation worse not better.

The Joint Committee on Human Rights, a senior committee within Parliament made up of senior MPs and peers, interviewed various experts earlier this month. Their findings would have made difficult viewing for the Prime Minister.

Karen McCartney, who helps implement the Government's current anti-extremism 'Prevent' strategy in schools, was asked how effective the government's plans to regulate out-of-school education settings for children (like Sunday schools and youth groups) would be. Her answer? They "will not prevent [extremist] things happening" and will "cause more harm than good".

When asked about the need for the new counter-extremism legislation proposed by the government, especially schools, McCartney said that in her extensive experience, "I have not come across a situation in which we have had to think of other options; the legislation that is available is more than adequate, as far as I am concerned." In other words: the current legislation works, and the government's attempts to add to it will create problems, not solve them.

Prof Louise Richardson, vice-chancellor of Oxford University and a leading counter-terrorism academic, practically pleaded with the government to scrap its plans. "My best advice would be: do not legislate," she said. "Too often, counterterrorist legislation is cast in security terms, or sometimes military terms, and has unintended negative consequences."

The damage the government's plans would cause – especially because they would suppress free speech – quickly became something of a theme. Christine Abbott, from Birmingham City University, articulated at length the strategy's flaws: "The risk in all this is that we drive debate underground in one way or another, be that into quiet corners that are in no way regulated in the physical space or in the virtual space of social media... if we suppress open dialogue and debate in our institutions, the risk is that it will go elsewhere in ways that are out of sight, uncontrollable and potentially much more risky."

A particular issue arose around the government's definition of extremism. Violent extremism is relatively easy to identify – terrorism, attempts to join ISIS, and other ideologically motivated attacks. But the government is now attempting to define 'non-violent extremism', ever since David Cameron made the startling claim in May last year that "for too long, we have been a passively tolerant society, saying to our citizens 'as long as you obey the law, we will leave you alone.''' (It's not really clear what he means by this, but it almost sounds like a criticism of the rule of law, which – ironically – would make Cameron an extremist, under the government's own definition.) And it is here that the government is getting itself tied in knots; it is attempting to bring in wide-ranging powers, based on a vague definition on 'non-violent extremism', rather than to make specific laws to target specific dangerous activity – surely the first rule of law-making.

Unsurprisingly, the experts are not impressed. Richardson criticised the government's current definitions of extremism (upon which the new proposals are based), calling them "deeply problematic." Strikingly, she went so far as to say that the government's definitions were so badly drafted that Oxford University didn't even try to enforce them, saying that if they did: "we would have to burn all our books by Plato and refer half our philosophy department." McCartney declared that she doubted "whether it is possible to define [extremism] clearly" – effectively damning the government's whole strategy.

So for all the Prime Minister's fighting talk last Wednesday, the government's plans seem to have tripped over the starting blocks. If the government is going to properly tackle extremism and terrorism in society, it will take more than strongly-worded speeches. It may even take a complete redrafting of their proposals.