The UK's commission on extremism has launched an investigation into tougher measures to prevent hate behaviour.
The Commission for Countering Extremism (CCE) believes there are gaps in the law allowing extremists to "sow divisions" and are looking into whether a new law could be introduced.
It will be examining whether it is possible to ban behaviour that leads people to hate each other.
The former head of counter-terrorism, Sir Mark Rowley, will lead the legal review.
The commission has found evidence of a number of incidents where hateful behaviour has happened but failed to meet the threshold to be considered a crime under the current law.
Incidents include protests by extremist organisations that encourage hostility and online abuse to other groups.
The abuse in these cases is not covered under the UK's terrorism legislation or hate laws.
Victims repeatedly told the CCE that they felt let down by the authorities and are concerned that existing powers are not being used effectively or consistently.
"Hateful extremism threatens our ability to live well together,” Sara Khan, the head of the commission, said.
"From inspiring acts of violence and terrorism, to the incitement of hatred and hostility often aimed at those with a protected characteristic, extremists are having a devastating impact on victims, on cohesion in our towns and cities and in undermining the social fabric and democratic norms of our country. Hateful extremism demands a response.
"Yet despite this, our ability to counter repeat and persistent offenders is inconsistent and often ineffective.
"When extremists engage in terrorist activity, they are often caught by robust counter-terrorism legislation. But when they incite hatred, engage in persistent hatred or justify violence against others, extremists know they will not cross over into the threshold of terrorism.
"As a result, many extremist actors and organisations, whether far-right, Islamist or other, continue to operate with impunity in our country both online and offline.
“This is why I am launching a review to examine the effectiveness of existing legislation."
Mr Rowley will be looking at existing laws and how they are used to see if a new offence could be created.
"Extremism, hate crime and terrorism have all been increasing challenges for our communities and society as a whole," he said.
"While I was in post as head of counter-terrorism policing for four years, I knew that we had strong counter-terrorism system, resources and laws in place.
“However, I increasingly realised that nationally we are less experienced and ready to address the growing threats from hateful extremists."
He will report his findings later in the year.
The CCE was launched in March 2018 following the London Bridge terror attacks in 2017.
It followed a commitment in the Queen’s Speech in 2017 to establish a commission “to support the government in stamping out extremist ideology in all its forms, both across society and on the internet, so it is denied a safe space to spread.”
The Commission’s flagship report Challenging Hateful Extremism was published last October.