Amnesty International is calling for a review of hate crime laws and improvements in training for police on how to deal with the offences.
The group says the measures are needed to combat a problem that is "under-reported and under-resourced".
In a briefing published a year on from the EU referendum, the organisation raises the alarm about incidents in which victims were targeted based on disability, race, religion, sexual orientation and transgender identity.
It also highlights cases of sectarian-motivated hate crimes in Northern Ireland.
Amnesty's paper, produced following a study by researchers at the University of Leicester, says many hate crime victims are not reporting abuse.
It argues that training of police officers across the country is inconsistent and conviction rates are low.
The study also points to figures suggesting a lower proportion of hate crime victims are satisfied with the police response in terms of fairness and effectiveness compared to general crime victims.
Kate Allen, director of Amnesty UK, said: "The rise of hate crime in the UK is of significant concern for a number of reasons - and the time is now to put a stop to it.
"Every year hundreds of thousands of people in the United Kingdom are attacked and harassed - physically or verbally - because they are perceived as 'different'.
"All people of all identities should be able to go about their lives in peace, without the fear of being abused or harassed by those who seek to sow hatred and division."
She added: "In recent weeks, attacks in London and Manchester have attempted to undermine the very fabric of our society.
"In their wake, we have seen reports of a rise in demonising language and dangerous comments that can cause real harm to real people. Now, more than ever, we must stand together against this hatred.
"We are now calling for police to receive increased training in how to respond to hate crime and support victims, for more resources to assist investigation and prosecution, and for more awareness in how victims can report hate crimes."
Concern around hate crime intensified in the days after the referendum a year ago.
Figures showed the number of racially and religiously aggravated alleged offences logged by forces in England and Wales in July 2016 was 41% higher than in the same month of the previous year.
A total of 62,518 hate crimes were recorded by the police in England and Wales in 2015/16, an increase of 19% compared with 2014/15.
A Home Office spokeswoman said: "There is no excuse for any form of intolerance and we are clear that anyone who commits a hate crime should be prosecuted.
"We already have a strong legislative framework to tackle hate crime but we are determined to do even more.
"This is why last year the Home Secretary published our hate crime action plan and asked Her Majesty's Inspectorate of the Constabulary to assess the police response to ensure it is dealt with effectively and efficiently."
Assistant Chief Constable Mark Hamilton, National Police Chiefs' Council lead for hate crime, said: "Everyone should be able to live their life free from hate crime and we continue to work to reduce the harm it causes.
"We welcome this research, as part of our approach to hate crime is to work closely with academics to better understand its complex origins and the impact it has on victims and our society.
"The UK has one of the most robust responses to hate crime anywhere in the world and our efforts are regularly praised by international observers.
"We have worked hard with partners to improve the service to victims and, despite the successes, we know there is still much to do."