Cambridge University's Students' Union said it is "alarmed" by claims that police 'tried to spy' on its members.
The Guardian newspaper has obtained a video of an officer trying to recruit an informant to target protest groups.
The Students' Union said it "condemned" the action and wants the government to look at how UK security forces use surveillance.
The National Union of Students (NUS) described it as "an absolute scandal".
The NUS said it undermines students' right to protest and demands to know just how widespread the practice is.
The Guardian claims police officers tried to spy on students at Cambridge University.
Footage obtained by the newspaper appears to show an officer trying to persuade an activist to become an informant in return for money.
The officer asks for information on potential supporters of groups including UK Uncut, the English Defence League, Unite Against Fascism and anti-fracking demonstrators.
He requested names of students going to protests and lists of the vehicles they were using.
But the would-be informant was secretly filming the meeting to expose what was going on.
Cambridge University declined to comment, saying it's a police matter.
A spokesman for the county's police force said:
"Officers use covert tactics to gather intelligence, in accordance with the law, to assist in the prevention and detection of criminal activity."
Guardian editor Alan Rusbridger will appear before MPs next month to answer claims his publication of Edward Snowden's security leaks has threatened national security.
His calling to the Home Affairs Select Committee comes after the head of MI6 told a separate House of Commons body the release of the US surveillance disclosures had put "operations at risk".
A Guardian spokesperson confirmed: "Alan has been invited to give evidence to the Home Affairs Select Committee and looks forward to appearing next month."
Two Conservative MPs have written to the editor of the Guardian to urge him to "acknowledge the devastating assessment" by Britain's spymasters of the damage caused by the publication of leaks by the former US intelligence operative Edward Snowden.
Tories Julian Smith and Stephen Phillips called on Alan Rusbridger to clarify whether he had "acted on every security concern raised by Government" over news stories.
They wrote that Rusbridger "fails to acknowledge the devastating assessment of the damage done to the national security of the United Kingdom by The Guardian's reporting of the Snowden leaks."
Yesterday MI6 chief Sir John Sawers said the Edward Snowden's leaks "have been damaging and put operations at risk."
Edward Snowden's leaks of UK surveillance programmes have been the "most catastrophic loss to British intelligence ever", according to David Omand, the former head of British listening post GCHQ and one-time adviser to Number 10.
His comments follow a warning from the new head of MI5, Andrew Parker, that revealing the "reach and limits" of GCHQ's activities causes enormous damage and gives an advantage to terrorists.
Omand said Snowden's leaks of 58,000 top-secret British security documents and secret US files was "seriously, seriously damaging".
He told the Times: "The assumption the experts are working on is that all that information or almost all of it will now be in the hands of Moscow and Beijing."
The Daily Mail has taken a swipe at the Guardian after the Director General of MI5, Andrew Parker said that leaks such as those from former NSA worker Snowden gave terrorists the, "gift they need to evade us."
NSA whistleblower Edward Snowden has denied claims he was the source of a leak about a key Middle East listening post.
The Independent reported that the facility allegedly collects emails, phone calls and web traffic on behalf of western intelligence agencies, which is why the government asked the Guardian to destroy files relating to Snowden.
In a statement to the Guardian journalist Glenn Greenwald, Mr Snowden has blamed the Government for the leak:
Guardian newspaper editor Alan Rusbridger said the decision to detain David Miranda "seems to me a clear misuse of a law."
Speaking at the Edinburgh International Book Festival, he called for a wider public debate about mass surveillance, praised the value of the information leaked by whistleblower Edward Snowden and described US soldier Bradley Manning's 35-year sentence "staggering".
Mr Rusbridger said the "strong suspicion" has to be that the detention of Mr Miranda at Heathrow Airport was "quite a carefully planned operation and wasn't random".
"There has to be a debate. There hasn't been much of a debate in this country yet because everyone is a bit complacent about it," he said. "In the end it's for people to decide."
The Guardian has welcomed what it called a "partial victory" after David Miranda, who was held at Heathrow Airport under anti-terror laws, was granted a limited injunction by the High Court.
A Guardian News & Media spokesperson said: "We welcome this partial victory but have grave concerns that today's judgment allows police to examine without any legal oversight journalistic material seized from David Miranda.
"It remains our position that David Miranda was involved in legitimate journalistic activity."
US intelligence chief James Clapper has said the law that allows American government agencies to collect communications from internet companies only permits the targeting of "non-US persons" outside the United States.
The response comes after The Guardian reported The National Security Agency had obtained direct access to the systems of Google, Facebook, Apple and other US internet giants, as part of a previously undisclosed program called PRISM.
PRISM allows officials to collect material including search history, the content of emails, file transfers and live chats.
Mr Clapper, the director of national intelligence, said in a statement the story, which also appeared in the Washington Post, contained "numerous inaccuracies," but did not offer any details.