The latest government figures showed a significant rise on yesterday’s case rate of 33,904.
It brings the UK’s total number of Covid cases to 131,373.
However, separate figures published by the Office for National Statistics show there have been 156,000 deaths registered in the UK where Covid was mentioned on the death certificate.
Between 23.6 million and 24.4 million Covid infections have been avoided thanks to the programme which has so far administered almost 74 million jabs in England.
More than 82,100 hospitalisations have also been directly averted thanks to the drive.
Dr William Welfare, Covid incident director at PHE, said on Thursday: “The pandemic is not over but vaccination is weakening the link between infection and serious illness.”
A total 73,982,159 vaccines had been given in England as of Wednesday, government figures show.
The number of pregnant women getting a Covid-19 vaccination has also risen by a fifth in recent weeks.
It follows a concerted effort by health officials to reassure expectant mothers about the safety of getting a jab.
A total of 62,311 pregnant women had come forward and received their first dose by the end of July, PHE said.