This will likely be much higher when figures across all settings - including care homes and the wider community - are released.
Scotland reported 43 new cases and no deaths, while Wales reported 18 cases and two deaths.
The paper said the new body will be called the Institute for Health Protection and will become "effective" next month, although it will take until next spring to complete.
The agency - set to launch on Tuesday - will merge some of Public Health England's (PHE) pandemic response work with the coronavirus test and trace system.
Tory peer Baroness Harding, the ex-TalkTalk boss who now runs NHS Test and Trace, is being tipped to lead the organisation, the paper said.
The move has reportedly been spurred by political dissatisfaction with PHE's handling of the coronavirus pandemic, including testing and the way deaths are counted, but some experts fear that it constitutes a political move to find a scapegoat for the government's own failings.
The move also comes amid fears of a second Covid wave this winter, with parts of the United Kingdom grappling with lockdowns as infections rise.
The future of public health in England is set to be announced later by Health Secretary Matt Hancock.
"With more than 1,000 new United Kingdom cases of Covid-19 being recorded for the fifth day in a row, we must seriously question whether now is the right time for undertaking such a seemingly major restructure and detract from the very immediate need to respond to the pandemic", said Dr Chaand Nagpaul, chair of the British Medical Association's ruling council, according to the paper.
"The Prime Minister and Secretary of State wish to recreate an organisation with a sole focus on health protection and to bring together our health protection services with the budgets and people of the NHS test-and-trace programme to create a new national institute for health protection".
Other aspects of its operations, such as tackling obesity, could be handed over to councils and family doctors, the newspaper said.
Responding to reports that Public Health England is to be replaced, a No 10 spokesman said on Monday: "We have always said we must learn the right lessons from the crisis and act to ensure Government structures are fit to cope".
Public health experts - including chief medical officer Prof Chris Whitty - have said that PHE has been affected by underfunding over recent years as a result of the government's decade-long austerity drive, which has led to a big reduction in headcount.
A government source told The Sunday Telegraph: 'One of the many problems with PHE is that it has been spread too thin during the full pandemic.
"But I would make the point that PHE have played an integral role in our response to this unprecedented pandemic, working on important issues such as detection, surveillance, contact tracing and testing".
'Instead of having an organisation that is constantly on alert for pandemics you have an organisation that has been concentrating on prevention of ill-health'.
Health officials are also furious with PHE for counting all deaths from Covid, rather than just those within the first 28 days of contracting the virus.