University staff including lecturers, chaplains and porters are being asked to inform the police about Muslim students who are depressed or isolated under new guidance for countering Islamist radicalism.

The move has resulted in deep discomfort among university lecturers and student union officials who wish to combat terrorism but say the new strategy is an infringement of students' civil liberties.

Officials implementing the government's revamped Prevent strategy are training frontline university employees in how to spot students vulnerable to extremism. Documents handed to staff claim that students who seem depressed or who are estranged from their families, who bear political grievances, or who use extremist websites or have poor access to mainstream religious instruction could be at risk of radicalisation.

The National Union of Students has told its officers that they do not have to provide police with details about students unless they are presented with a warrant.

Local authority workers and police officers have been introducing the new strategy over the last month. Inquiries by the Guardian show that colleges in Lancashire and London have been approached by police and local authorities.

James Haywood, president of Goldsmiths college students' union in south-east London, met two Prevent officials last week. He said they began by asking about Muslim students and whether the college had problems with its Islamic Society.

"We were appalled to have Prevent officers asking us to effectively spy on our Muslim students. To pass on details of a student who the police consider 'vulnerable' is not only morally repugnant but is against the confidential nature of pastoral support. After the rise of hate groups such as the English Defence League, and the recent massacre in Norway, why are Prevent not also telling us to refer on students who have an irrational hatred of Islam?" he said.

Universities that agree to the renewed version of the scheme are trained to refer "at risk" students to Prevent officials. The student is then monitored by a panel including a detective from Scotland Yard, who assess any potential terror threat. The student is not made aware at any stage that they are under investigation.

The Prevent strategy was first launched in 2007 and sought to stop people becoming terrorists or supporting terrorism. It was relaunched in June and refocused on universities after it was revealed in January that "underpants bomber" Umar Farouk Abdulmutallab had studied at University College London.

In June, the home secretary, Theresa May, said the original strategy had resulted in "complacency around universities" and that Labour had not been "sufficiently willing to recognise what can be happening on … campuses".

A recent government report said there were 40 English universities where there could be a "particular risk" of radicalisation, although the names of the universities have not been released.

The University and College Union (UCU) said that the government's strategy risked damaging the relationship between staff and students. "Staff have made it quite clear that they do not wish to police their students or engage in any activity that might erode the trust between them and students," it said.

The Federation of Student Islamic Societies, an organisation that provides support to Muslim students across the UK and Ireland, said: "Spying on a completely innocent group of people is an affront to our human rights. Islamic Societies and Muslim students make a positive contribution to British civic life – and they must be supported.

"We have continued in our dialogue with the government to say that engaging with Muslim students, not spying on them, is what will make our country safer and more cohesive. Prevent is long-discredited now in civic society. We need an intelligent approach to security policy rather than one driven by political motives."

Professor Ted Cantle, executive chair of the Institute of Community Cohesion, warned that the government's new policy risked stigmatising Muslims.

"The government shouldn't be bringing in people who have little understanding of the Muslim community and radicalisation and asking them to pronounce and point the finger," he said.

The Home Office defended the new policy. "The Prevent programme is about stopping people being drawn into terrorism. We all have an interest in that and we expect universities and colleges to play a full and constructive role in that aim.

"The new Prevent strategy helps universities and colleges fulfil their duty of care to their students. The government has not received any representations from educational institutions saying they will not take part."