Waving a Palestinian flag on British streets “may not be legitimate” if it is deemed to be a show of support for acts of terrorism, the Home Secretary has told police chiefs.

Suella Braverman has urged officers to use the “full force of the law” against shows of support for Hamas or bids to intimidate the UK’s Jewish community in the wake of the attack on Israel.

The flare-up of violence in the Middle East has led to shows of public solidarity on both sides, with vigils held to remember those killed in Israel as well as protests demonstrating in favour of Palestinian rights.

In a letter addressed to chief constables in England and Wales, Mrs Braverman said: “Sadly, experience indicates that whenever Israel is attacked, Islamists and other racists seek to use legitimate Israeli defensive measures as a pretext to stir up hatred against British Jews and increase fear within the Jewish community”.

The Cabinet minister set out examples of protest that she said could amount to public order offences, including targeting Jewish neighbourhoods, waving pro-Palestinian or pro-Hamas symbols and chanting slogans that could be interpreted as anti-Israeli.

The senior Conservative politician said: “I encourage all chief officers to ensure that any protests which could exacerbate community tensions by way of offensive placards, chants, or behaviours that could be construed as incitement or harassment, have a strong police presence to ensure perpetrators are appropriately dealt with, and that communities feel protected.”

It comes after Prime Minister Rishi Sunak vowed to “hold people to account” if they are found to be supporting Hamas in Britain.

Mr Sunak told broadcasters on Tuesday that police have been given “clear guidance” to “clamp down on any behaviour that falls foul of the law”.

The Israel-Gaza conflict has sparked reactions in UK communities, with three people arrested during protests and vigils on Monday evening.

Hundreds of pro-Palestinian protesters gathered outside the Israeli embassy in Kensington to demonstrate on that same evening, letting off fireworks, lighting flares and chanting “Israel is a terrorist state”, “Free Palestine” and “Allahu akbar”.

Only a few miles east of that demonstration, more than 4,000 people are estimated to have joined a vigil outside Downing Street organised by the Board of Deputies of British Jews and the Jewish Leadership Council.

Mrs Braverman, in her letter to police chiefs sent on Tuesday, said she recognises that decisions on arrests are “rightly an operational matter for police”, while urging forces to “use all available powers to prevent disorder and distress to our communities”.

“It is not just explicit pro-Hamas symbols and chants that are cause for concern,” said Mrs Braverman, who on Monday visited Golders Green, a north London area with a large Jewish population.

“I would encourage police to consider whether chants such as ‘From the river to the sea, Palestine will be free’ should be understood as an expression of a violent desire to see Israel erased from the world, and whether its use in certain contexts may amount to a racially aggravated Section 5 public order offence.

“I would encourage police to give similar consideration to the presence of symbols such as swastikas at anti-Israel demonstrations. Context is crucial.

“Behaviours that are legitimate in some circumstances, for example the waving of a Palestinian flag, may not be legitimate such as when intended to glorify acts of terrorism.

“Nor is it acceptable to drive through Jewish neighbourhoods, or single out Jewish members of the public, to aggressively chant or wave pro-Palestinian symbols at.

“Where harassment is identified, I would encourage the police to take swift and appropriate enforcement action.”

On Saturday, Hamas sent fighters across the border into Israel and fired thousands of rockets in an unprecedented incursion, which also saw a music festival targeted.

Since the weekend’s atrocities, Israel has cut Gaza off from deliveries of food, fuel, medicine and other supplies and has launched retaliatory air strikes on the 25-mile stretch, which is home to 2.3 million people.

At least 1,600 lives have already been claimed on both sides, and perhaps hundreds more.