The UK Health Security Agency said vaccines are breaking the link between cases and hospitalisations nationally, but urged people to continue to be cautious.
That was 270 more than the 286 cases recorded the week before.
Those identified in the latest week were among at least 11,304 cases of the variant recorded across Yorkshire and The Humber – the third-worst affected of England's nine regions.
The North West continued to have the highest numbers identified, with 38,189 Delta variant cases recorded there.
Across the UK, 35,204 more cases were recorded in the last week to reach a total of 111,157 – a 46% increase.
Of these, 42 are the so-called Delta plus variant, which India’s health ministry has said spreads more easily, binds more easily to lung cells and is potentially resistant to some drug therapy which can help neutralise the virus.
But while the Delta variant now accounts for around 95 per cent of new cases sequenced in the UK, PHE said vaccines continue to have a “crucial effect on hospital admission and death”.
A further 514 people were admitted to hospital in England with Covid-19 in the week up to June 21. Of these, 304 were unvaccinated.
Dr Jenny Harries, chief executive of the UK Health Security Agency, said: “Through the success of our vaccination programme, data suggest we have begun to break the link between cases and hospitalisations. This is hugely encouraging news, but we cannot become complacent.
“Two doses of vaccine are far more effective against Covid-19 than a single dose, so please make sure that you come forward to get your second dose as soon as you are invited."
PHE said the figures for variants this week are likely to be an underestimate owing to an operational issue being investigated by the Wellcome Sanger Institute on potential cross-contamination of a number of positive Covid-19 samples.
It said these samples were PCR tested before they were sent to the Sanger Institute, meaning people have received their correct test result and positive cases told to isolate.