There are warnings from Ofsted that further education providers are “falling short in protecting learners from risk of extremism”.
The education watchdog has been examining how well colleges implement the Prevent counter-extremism strategy.
In one case, inspectors said a student had watched “terrorist propaganda video” in a resource centre.
Ofsted’s Paul Joyce said there was “poor practice that I’ve no doubt would shock parents and learners alike”.
The report from Ofsted, based on visits to 37 further education and skills providers and 46 regular inspections or monitoring visits, concluded that too many students were at risk of “radicalisation and extremism”.
It found that general further education colleges and sixth-form colleges were “making good progress” with carrying out the Prevent duties on tackling extremism.
But there were particular concerns about small, independent providers, who might be “leaving learners at risk”.
Ofsted inspectors warned of a lack of safeguards for internet use and found examples where students had been able to “bypass” online security settings to visit websites “selling firearms” or “promoting terrorist ideology”.
“These included one isolated instance of a learner viewing a terrorist propaganda video in the provider’s learning resource centre,” the report says.
This is understood to be a video from so-called Islamic State showing a beheading.
The Ofsted report says some colleges have adopted a tougher line on internet access, such as “stringent firewalls” and regular checks on attempts to access inappropriate websites.
And there are colleges that block internet access on students’ personal devices when they are on college premises.
There were also some concerns over checks on external speakers.
But, overall, inspectors found that outside speakers helped students to learn about different views, which promoted “tolerance, respect and democracy”.
Ofsted’s deputy director for further education and skills, Paul Joyce, said that most leaders of FE and sixth-form colleges were making “quick progress” in carrying out their duties under the Prevent strategy, introduced for colleges last year.
But he said it was worrying that for some providers “the progress made in implementing the duty has been slow”.
David Corke, the Association of Colleges’ director of education and skills, said colleges have been “working incredibly hard to implement the duty, and they will continue to do so as the threat of radicalisation and terrorism is ever present”.
“The safeguarding of students is of paramount importance for further education and sixth-form colleges,” he said.
But Sally Hunt, general secretary of the UCU lecturers’ union, said that colleges had to cope with “vague definitions” and “inconsistent advice” in the debate about challenging radicalisation and protecting free speech.
“The Prevent duty risks doing more harm than good by shutting down debate on contentious topics and creating mistrust between teachers and students,” she said.
“College teachers have always taken their duty of care to students very seriously, so the focus on implementing the Prevent duty is both unnecessary and potentially counterproductive.”
Skills Minister Nick Boles said: “While the majority of providers have worked hard to implement the safeguards effectively, we recognise there is still further work to do in making the government-funded guidance and training as consistent as possible.”