England lost to Italy on penalties in the final of Euro 2020 at Wembley Stadium on Sunday, with Saka, Sancho, and Rashford all missing their penalties.
The trio were subjected to abuse online and now four people have so far been arrested as investigations into the matter continue.
In a statement issued to the PA news agency, The UK Football Policing Unit (UKFPU) said: “Following England’s defeat against Italy on Sunday a torrent of racist comments aimed at some of the team’s black players appeared on platforms including Facebook, Instagram, and Twitter.
“A hate crime investigation is underway by the UKFPU, with a dedicated team of investigators working their way through a large number of reports from across the country.
“So far, dozens of data applications have been submitted to social media companies and four people have been arrested by local police forces.”
Chief Constable Mark Roberts, the National Police Chiefs’ Council football policing lead, said: “The racial abuse aimed at our own players following Sunday night’s game is utterly vile and has quite rightly shocked and appalled people across the country.
“Our England team have been true role models during the tournament, conducting themselves with professionalism and dignity. I’m disgusted there are individuals out there who think it’s acceptable to direct such abhorrent abuse at them, or at anybody else.
“The UKFPU investigation is well underway and work continues to identify those responsible. We are working very closely with social media platforms, who are providing data we need to progress enquiries.