Indian variant latest
The figures released on Thursday have risen from 520 cases recorded by PHE up to 5 May.
Most of the cases have been detected in England, with 1,255 cases recored.
There have also been 35 cases detected in Scotland, 12 in Northern Ireland and 11 in Wales, according to PHE.
Broken down by region, more than 30 percent of cases are in London, followed by 25 percent in north-west England, 12 percent in eastern England, 10 percent in the East Midlands and eight percent in the South East, PHE said.