Around 600 extra people a week have died in the early part of 2013 compared with the last five years, adding up to around 10,000 people, The Times reported.
Overall there was an increase of 5% in the mortality rate between early 2012 and early 2013 - up by 23,400.
The figures were detailed in a report by PHE seen by the newspaper.
The report said that 2013 so far "stands out as noticeably worse than any recent year", The Times said.
However, the current weekly number of deaths is "within levels expected" for this time of year, PHE said.
Health experts have suggested the spike in deaths among those aged 85 years and older could be down to cuts to council care, resistance to medication, or a levelling out in life expectancy.
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Professor John Ashton, president of independent health body the Faculty of Public Health, told the newspaper: "It will no doubt raise questions about access to clinical care among the frail elderly and whether it's not as good as it was.
He also suggested the elderly generation could have built up resistance to antibiotics after using them for decades or even that there was an accumulation of frail people "whose time has finally come".
A spokeswoman for PHE said: "As acknowledged in Public Health England's annual influenza report, the number of deaths during 2012/13 was high, especially amongst those 85 years and older and in deaths recorded as resulting from respiratory causes.
"We are currently undertaking further work to understand why there was a rise in mortality rates during the earlier months of this year and the causes behind this. The weekly number of deaths are currently within levels expected for this time of year."