The figures were confirmed today by Caroline Walker, chief executive of North West Anglia NHS Foundation Trust.
She said: “I can confirm that sadly 725 patients being cared for in our trust have passed away since we began reporting Covid-19-related deaths.
“There have been 233 at Hinchingbrooke Hospital and 492 at Peterborough City Hospital.
“All patients were aged 30 to 105 years old and the majority of those had pre-existing health conditions.
“Our thoughts and condolences remain with the patients' families and loved ones at this difficult time.”
All six of the deaths since September 3 occurred at Peterborough hospital, with no rise in the number of Covid deaths at Hinchingbrooke.
New figures published today by the Office for National Statistics (ONS) revealed that people who were fully vaccinated against Covid-19 accounted for only 1% of all deaths involving coronavirus which occurred in England in the first seven months of this year.
Of the 51,281 deaths involving Covid-19 which took place in England between January 2 and July 2, 640 (1.2%) were people who had received both vaccine doses.
This total includes people who had been infected before they were vaccinated.
Of these, 458 deaths (0.8% of the total number of deaths) were people who died at least 21 days after their second dose.
Just 256 deaths (0.5% of the total number of deaths) were people who were both fully vaccinated and who had their first positive PCR test at least 14 days after their second dose.
Some deaths are expected in vaccinated individuals, as the number of people who have received both doses is high and no vaccine is 100% effective, the ONS said.
A detailed breakdown of data is available for 252 of the 256 people who died after having received both jabs and who first tested positive at least 14 days after the second dose – what the ONS describes as “breakthrough” deaths.
It shows that just over three-quarters of these deaths (76.6%) occurred in those who were clinically extremely vulnerable.
Some 61.1% of breakthrough deaths occurred in males.
Professor Gino Martini, chief scientist for the Royal Pharmaceutical Society, described the figures as “extremely reassuring”.
He said: “The data shows that people are much better protected from the virus after two doses, and hopefully this will inspire others to get the vaccination to protect themselves and others."