More than 3,000 hate crimes and incidents were reported to police from 16-30 June this year, a 42% increase on the same period in 2015, National Police Chiefs' Council figures show.
It comes amid reports of what David Cameron called "despicable" hate crimes after the EU referendum on 23 June.
At the peak on 25 June, 289 hate crimes and incidents were reported across England, Wales and Northern Ireland.
Assistant Chief Constable Mark Hamilton said the "sharp rise" was unacceptable.
UK police forces were asked to disclose weekly hate crime numbers after an increase in reports to True Vision, a police-funded website.
In total, there were 3,076 reported hate crimes and incidents in the second half of June, compared to 2,161 in the same period in 2015.
The National Police Chiefs' Council 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".
Last month, following the UK vote to leave the EU, Mr Cameron condemned incidents including "verbal abuse hurled" at ethnic minorities, and "despicable" graffiti on a Polish community centre.
In Plymouth, a shed next to a Polish family's house was set on fire on Wednesday night.
No-one was hurt but the property was damaged, and the family received a note telling them to "go back" to Poland.
Ewa Banaszak, 22, whose father and two younger sisters were in the home at the time of the fire, said: "It has been very intense after the referendum, with people saying 'go back to your own country'.
"We've had verbal comments over the last couple of years but it has intensified."
She said the family had been supported by the public and police.
Meanwhile, counter-terrorism officers are investigating five incidents in which white powder was sent to Muslim centres, mosques and government buildings in London.
One of the recipients was Muslim peer Lord Ahmed, who was sent hate mail along with white powder, causing a security alert at Parliament.
Scotland Yard has said three of the packages, all of which arrived on Thursday, were found to be "not noxious or suspicious".
True Vision defines hate crimes as offences where a victim is targeted because of criteria including their race, religion, sexual orientation or disability.
ACC Hamilton said the increase in hate crimes "undermines the diversity and tolerance we should instead be celebrating".
"Everyone has the right to feel safe and confident about who they are and should not be made to feel vulnerable or at risk," he said.