The UK’s official human rights watchdog has written to ministers and police expressing concern at a potentially “heavy-handed” approach to protests about Gaza and urging clearer guidance for officers in enforcing the law.

In the letter to Yvette Cooper, the home secretary, and Mark Rowley, the head of the Metropolitan police, the Equality and Human Rights Commission (EHRC) said the perception that peaceful protest could attract disproportionate police attention “undermines confidence in our human rights protections”.

Kishwer Falkner, the EHRC chair, wrote that it was vital that any policing of protests was both proportionate and based on clear legal tests.

The letter raised concerns about “reports of police engagement with individuals participating in forms of protest that are not linked to any proscribed organisation”.

It cited as an example the case of Laura Murton, first revealed by the Guardian. Keny police threatened her with arrest under the Terrorism Act for holding a Palestinian flag and having signs saying “Free Gaza” and “Israel is committing genocide”.

Murton filmed police telling her that even such general statements “all come under proscribed groups, which are terror groups that have been dictated by the government”.

During the exchange, one officer said the phrase “Free Gaza” was “supportive of Palestine Action”, that it was illegal “to express an opinion or belief that is supportive of a proscribed organisation”, and that she had committed that offence with her signs.

Falkner wrote: “Whilst we acknowledge police expertise in assessing security risks, we want to emphasise that any interference with protest rights must be lawful and assessed case by case.

“Heavy-handed policing or blanket approaches risk creating a chilling effect, deterring citizens from exercising their fundamental rights to freedom of expression and assembly through fear of possible consequences.

“This concern extends beyond those directly affected by police engagement to the broader health of our democracy, because the perception that peaceful protest may attract disproportionate police attention undermines confidence in our human rights protections.”

Falkner urged ministers and police to make sure all officers were given “clear and consistent guidance on their human rights obligations in relation to protest”, which should “ensure that the appropriate balance is maintained between public safety and the protection of essential human rights”.

Murton told the Guardian last week that her solicitors had issued a letter of claim on her behalf to the chief constable of Kent police, in what was also said to be a move to remind other police forces of their responsibilities towards peaceful protests.

Falkner said in a statement: “The right to peaceful protest is fundamental to our democracy and must be protected even when dealing with complex and sensitive issues.

“We recognise the genuine challenges the police face in maintaining public safety, but we are concerned that some recent responses may not strike the right balance between security and fundamental rights.

“Our role as the national human rights institution is to uphold the laws that safeguard everyone’s right to fairness, dignity and respect. When we see reports of people being questioned or prevented from peaceful protests that don’t support proscribed organisations, we have a duty to speak out.”

The Liberal Democrats called on Cooper to act swiftly. Lisa Smart, the party’s home affairs spokesperson, said: “The lack of clarity that has been given to police officers has led to confusion, increasing tensions and risks creating a chilling effect on freedom of speech.

“The home secretary needs to step in and give officers, often dealing with incredibly complex and sensitive situations, clear direction as to what is expected of them at protests.

“Without that officers will be left exposed and those exercising their democratic rights worried about the consequences.”

The warning comes in the context of wider police operations targeting protesters who, unlike Murton, appear to directly express support for Palestine Action, which is illegal given the group’s banned status.

Membership of, or support for, the group is a criminal offence punishable by up to 14 years in prison under the Terrorism Act.

The group was proscribed last month after incidents including one in which four people were arrested over damaged caused to two Voyager aircraft at RAF Brize Norton in Oxfordshire.

In the latest of a series of mass protests against the decision, more than 500 people were arrested in London last Saturday, almost all for displaying placards or signs allegedly supportive of Palestine Action. Half of those arrested were aged 60 or above, according to police figures. On Friday night the Metropolitan poice said a further 60 people would be prosecuted for “showing support for the proscribed terrorist group Palestine Action”.

Amnesty International UK said that while it welcomed the EHRC letter, the watchdog had “failed to acknowledge the hundreds of people unfairly arrested for peacefully exercising their right to free expression”.

Sacha Deshmukh, the organisation’s chief executive, said: “This isn’t just about the chilling effect on freedom of speech for people ‘not linked to any proscribed organisation’, as the EHRC states, it’s also about the excessive policing of citizens’ right to protest against a decision made by their elected government.

“Under international human rights law, protest speech should only be criminalised if it incites violence, hatred or discrimination. Holding a placard and peacefully stating opposition to a government decision to proscribe an organisation cannot realistically be treated as an example of incitement.”

Downing Street has justified the ban on Palestine Action by saying it is “a violent organisation that has committed violence, significant injury, extensive criminal damage”, a description one of its co-founders has said is false and defamatory.

The Home Office said the issues the EHRC had raised were an operational matter for the police. The Met referred the query to the Home Office.