Dr Nepogodiev called for specified Covid and non-Covid hospitals or to use private facilities for surgery that is not coronavirus related.
The need to deep clean operating equipment between surgeries means the rate of people being treated will be reduced compared to before the pandemic.
And some hospitals are preparing for a second wave of infections by keeping large areas clear.
The Birmingham University report predicted hospitals will be working at about 80 per cent until September.
It said there was a three-part phased return to surgeries, with the cancelling of operations until this month being phase one and causing a 516,462-patient backlog.
The second phase, which will last until September, will more elective surgery but will add a further 141,271  people to the waiting list.
Matt Hancock: 'We proceed with caution and safety first'
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The final stage will see surgery rate rocket to more than 15 per cent than normal levels to try to stem the backlog.
An NHS England spokesman said: 'As the NHS responded to the once-in-acentury pandemic, hospitals had to treat more than 95,000 people for Covid-19.
'Now that the NHS has managed the first wave of this virus, there is clearly an important job to do to help people whose routine elective operation was postponed, which will involve permanent increases in staffing and bed capacity, as well as an ongoing partnership with independent providers.'
Last month the CovidSurg Collaborative at Birmingham University predicted there would be 28million cancelled surgeries due to Covid-19.
The study, published in the British Journal of Surgery found there were 2.4million cancellations each week due to the disruption. 
The huge financial strain facing the NHS comes after it was revealed private hospitals taken over by the health care giant at a cost of hundreds of millions of pounds to the taxpayer remain almost completely empty.
More than 8,000 private beds in England were bought up by ministers in March at an estimated cost of £2.4million a day, in anticipation hospitals would be overwhelmed.
The beds have been under public control for nearly 11 weeks, thought to have cost the taxpayer at least a staggering 150million already, with the figure rising every day.
But the health service's intensive care wards were not overrun during the peak of the pandemic and the majority of the private beds went unused.
Private hospitals are now meant to be operating as 'Covid-free hubs' to get back up and running for vulnerable people, including cancer patients.
But a senior consultant said last week 'very few' of these patients were being referred to the private hospitals, leaving them almost completely empty.
It has meant 'tens of thousands' of cancer patients - who need urgent treatment to boost their survival rates - are missing out on vital treatment every month.
Private hospitals taken over by NHS at a cost of hundreds of millions of pounds to fight the coronavirus pandemic are ‘sinfully empty’, claim medics. Pictured: The ICU wards at the hastily built Nightingale Hospital have barely been used throughout the crisis
Private hospitals taken over by NHS at a cost of hundreds of millions of pounds to fight the coronavirus pandemic are 'sinfully empty', claim medics. Pictured: The ICU wards at the hastily built Nightingale Hospital have barely been used throughout the crisis
The 8,000 beds are said to be costing the NHS £2.4million per day, according to the Mirror. They have been under public control since March 21, which was 10 weeks and 5 days, or simply 75 days, ago.
Rough estimates suggest taxpayers have already forked out £180million for the beds.
Karol Sikora, a consultant oncologist and professor of medicine at the University of Buckingham Medical School, told MailOnline: 'Once it became clear the private beds would not be needed for Covid patients, the idea was to use private hospitals as Covid-free zones. But that has only partly materialised. 
'Because the NHS is not doing surgeries, thousands of cancers are going undiagnosed. Surgery is needed in some cases to diagnose someone with the disease and get them started on their treatment.
Professor Karol Sikora (pictured) is consultant oncologist and professor of medicine, University of Buckingham Medical School
Professor Karol Sikora (pictured) is consultant oncologist and professor of medicine, University of Buckingham Medical School
'Because the patients are not being diagnosed, they are not coming through the system.
'We know there should be 30,000 new cancer patients every month - but this month there have been less than 5,000 that have come for treatment.
'It's not that there are less people with cancer, it's that they are not being diagnosed because of a bottleneck in the NHS.
'The whole thing has set us back a year, no other country has struggled this much to open healthcare back up. I don't know what's behind the bottleneck, maybe it's a staffing issue.'
Senior clinicians at private hospitals claim hundreds of the country's best doctors have been left 'twiddling their thumbs' during the outbreak – putting people's health at risk from other illnesses and postponed operations.
It has left private patients with no option but to join huge NHS waiting lists triggered by the pandemic.
Nigel Edwards, chief executive of the Nuffield Trust think-tank, said hospitals have only been able to carry out around '15 to 20 per cent' of surgeries, meaning up to 1.3million patients are missing out every month. 
In one case, a 78-year-old woman with breast cancer was denied surgery at a private clinic by the local NHS manager even though the hospital was empty, according to The Times. The patient was instead referred back to the NHS. 
Cancer Research says almost 2.5million patients have missed out on vital cancer tests and treatment due to shocking backlogs during the crisis.

UK patients face a TWO-YEAR wait for elective surgery with NHS backlog set to hit 650,000

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