The analysis included 14,019 cases of the Delta variant – 166 of whom were hospitalised – between 12 April and 4 June, looking at emergency admissions in England.
PHE said further work is underway to establish the level of protection vaccines offer against mortality, but said it was expected to be high.
Health and Social Care Secretary Matt Hancock said: “Our UK vaccination programme continues at pace and has already saved thousands of lives. It is our way out of this pandemic.
“This evidence of the effectiveness of two doses against variants shows just how crucial it is to get your second jab.
“If you have had your first dose but haven’t booked your second yet – please do so. It will help save lives and boost us on the road to recovery.”
PHE estimates suggest the vaccination programme has so far prevented 14,000 deaths and around 42,000 hospitalisations of older people in England.
‘Vaccines highly effective’
A separate study from Scotland has found that the risk of hospitalisation from the Indian variant is cut by 70 per cent for people who have been fully vaccinated.
The study by the University of Edinburgh and Public Health Scotland (PHS) suggested vaccines were more effective in protecting against the Kent strain.
However it also found “very few” over-65s testing positive for Covid, suggesting the jabs are protecting the most vulnerable.
The Scottish team calculated that for people who had two doses or who had their first dose at least four weeks ago, the risk of being hospitalised with the Kent variant was reduced by 72 per cent and the Indian variant by 62 per cent.
In community cases at least two weeks after the second dose, the Pfizer/BioNTech jab was found to provide 79 per cent protection against infection from the Indian variant, compared with 92 per cent against the Kent strain.
The Oxford/AstraZeneca vaccine offered 60 per cent protection against infection with the Indian variant compared with 73 per cent for the Kent variant.
Dr Jim McMenamin, the national Covid-19 incident director at PHS, said: “We do appear to show that delta variant does increase the risk of hospitalisation. However, what we are able to see is that our vaccines are still highly effective.
“These results provide early encouragement that two doses of either Pfizer/BioNTech or Oxford/AstraZeneca vaccines significantly reduce the risk of infection against both the alpha or new delta variants.
The findings are published as a research letter in The Lancet.
Researchers said a delay to the June 21 reopening would mean more people could get their second jab and gain further protection. Prof Aziz Sheikh, director of the Usher Institute and professor of primary care research and development at the University of Edinburgh, said: “Getting people second doses and giving people reasonable amounts of time is key here really.
“If there is a delay, that will give us the opportunity to widen coverage, and for those who have only got one dose what we want is a period of time where people can maximise their immune response.”