David Cameron’s counter-extremism bill, which will ban non-violent extremists, risks provoking a backlash in Britain’s Muslim communities and playing into the hands of terrorist recruiters, a government watchdog has warned.

David Anderson QC, the independent reviewer of terrorism laws, said the legislation to counter extremist ideology also risks legitimising state scrutiny of – and citizens informing on – the political activities of large numbers of law-abiding people.

His warning on Thursday comes as the prime minister’s counter-extremism taskforce meets in Downing Street and the House of Lords prepares to vote on rules banning extremist speakers from university campuses.

The counter-extremism bill, which is due to be published later this year, is aimed at “suppressing extremist activity”. It will include proposals for banning orders to outlaw extremist organisations, extremist disruption orders to restrict the activities of individuals, and closure orders to shut down premises used by extremists.

Cameron and the home secretary, Theresa May, have defined extremism as as “vocal or active opposition to fundamental British values”. It covers a range of activity not caught by the current law as terrorism, incitement to violence, stirring up hatred or abuse.

Anderson, in his annual report on the terror laws, said the restrictions to free speech in the proposals were likely to prove controversial.

“These issues matter because they concern the scope of UK discrimination, hate speech and public order laws, the limit that the state may place on some of our most basic freedoms, the proper limits of surveillance, and the acceptability of imposing suppressive measures without the protections of the criminal law,” wrote Anderson.

“If the wrong decisions are taken, the new law risks provoking a backlash in affected communities, hardening perceptions of an illiberal or Islamophobic approach, alienating those whose integration into British society is already fragile, and playing into the hands of those who, by peddling a grievance agenda, seek to drive people further towards extremism and terrorism.”

Anderson said the potential of the new law to affect those who are not its target is particularly important. He said that while ministers will justify the measures by saying they are only targeted at a handful of individuals and organisations, this does not address the dangers inherent in such an “overbroad law”.

He said: “If it becomes a function of the state to identify which individuals are engaged in, or exposed to, a broad range of ‘extremist activity’, it will become legitimate for the state to scrutinise [and the citizen to inform upon] the exercise of core democratic freedoms by large numbers of law-abiding people.

“The benefits claimed for the new law – assuming that they can be clearly identified – will have to be weighed with the utmost care against the potential consequences, in terms of both inhibiting those freedoms and alienating those people.”

The home secretary replied to the criticism by saying that she would respond to it formally in due course.