Doctors and other health professionals will be asked to identify people who are "vulnerable to being drawn into terrorism" as part of the government's redrawn counter-terrorism programme to be detailed on Tuesday.

The home secretary, Theresa May, will also try to deflect criticism that the £60m-a-year Prevent programme has been used to spy on the Muslim community by extending its coverage to the far right and animal rights extremists, as well as Islamist groups.

May has indicated that 20 of the organisations funded by the government over the past three years are to have their cash withdrawn after the decision to stop working with non-violent extremists.

David Cameron has pushed through the change despite opposition from Nick Clegg and Charles Farr, the head of the office of security and counter-terrorism, arguing that such engagement is like "turning to a rightwing fascist party to fight a violent white supremacist movement".

The argument within Whitehall has delayed the publication of the revised Prevent strategy for five months and it is believed that Cameron only finalised the document on Monday afternoon.

The Prevent programme was developed to combat home-grown terrorism after the 7 July bombings in 2005.

The final draft is believed to propose to "expand Prevent programmes to health bodies to draw on the expertise of medical professionals".

One "key message" of the document is that it is not a programme to spy on Muslim communities, but doctors will be asked to identify people who may be "vulnerable" to recruitment by terrorist groups.

The government is also expected to say that millions of pounds have been wasted on anti-extremism projects that did not produce any security benefits, and that the new strategy promises to "significantly scale up" work in prison. May says in her foreword to the policy paper that the coalition inherited a "flawed" programme, the Times reported.

The British Medical Association said doctors were allowed to breach patient confidentiality in the public interest – for example, if they thought someone was going to blow up a bus.

But a spokeswoman said the plan "goes a lot further and we would have an issue with that".

She said: "Doctors cannot look into the future and say how someone might behave This would threaten the trust of the doctor and … patient relationship.A doctor's role is to treat the patient in front of them, not predict how the patient will behave in future."

The doctors' concerns followed warnings from university vice-chancellors that May's push to clamp down on non-violent extremist speakers on campuses could lead to renewed freedom of speech rows and drive groups underground. Counter-terrorism officials are reported to have identified 40 universities that have been judged to be at particular risk of radicalising activity.

The home secretary accused universities of complacency over campus extremism and said of the Federation of Student Islamic Societies (Fosis): "They need to be prepared to stand up and say that organisations that are extreme or support extremism or have extremist speakers should not be part of their grouping."

Nabil Ahmed, president of Fosis, said the accusation was unjustified. "We have consistently taken measured steps to engage with key stakeholders, including members of the government, on the issue of radicalisation on campus," he said. "We find it disrespectful for commentators to throw around accusations of extremism so easily – especially when not only university vice-chancellors but David Willetts, the universities minister, himself have clearly elucidated how extremism is not widespread on campus, and have questioned whether universities are the 'trigger' for radicalisation."