The daily rate peaked the day after the Brexit result was announced, with 289 alleged offences
More than 3,000 hate crimes were reported to police across the UK in the second half of June - a 42% rise compared with the same period last year.
The daily rate peaked at 289 alleged offences on 25 June - the day after the EU referendum result was announced.
Data published on Friday by the UK's National Police Chiefs' Council (NPCC) give the most comprehensive insight into the nationwide picture so far.
Forces were asked to reveal weekly numbers after a series of reports sparked fears of a wave of xenophobic and racial abuse in the wake of the vote to leave the EU.
The first set of figures shows 3,076 hate crimes and incidents were reported to police between 16 and 30 June.
This was an increase of 915, or 42%, compared with the same period in June 2015.
The NPCC said the main type of offence reported over the fortnight was "violence against the person", which includes harassment and common assault, as well as verbal abuse, spitting and "barging".
The second and third most common types of incidents were public order offences and criminal damage.
The NPCC said that since then there has been a marked decrease in reports, but weekly figures will continue to be collated to monitor the situation.
Assistant Chief Constable Mark Hamilton, NPCC lead for hate crime, said: "We now have a clear indication of the increases in the reporting of hate crime nationally and can see that there has been a sharp rise in recent weeks.
"This is unacceptable and it undermines the diversity and tolerance we should instead be celebrating.
"Forces have been monitoring and managing hate crime more robustly since the attacks in Paris in 2015. We believe that greater awareness and confidence in the police response has contributed to this increase in reporting."
Mr Hamilton said police forces have heightened their response to hate crimes over the last 10 days.
"We are working locally and nationally with partners to reassure communities and tackle offending," he said.
"We will remain in close liaison with the CPS to ensure that the criminal justice system responds quickly and appropriately.
"Everyone has the right to feel safe and confident about who they are and should not be made to feel vulnerable or at risk."
Earlier this week, figures indicated that the number of hate crimes reported in London had risen by more than 50% in the days since the EU referendum result.