Research by the Institute for Public Policy Research estimated 19,500 people who should have been diagnosed had not been, because of missed referrals.
If hospitals could achieve a 5% increase in the number of treatments over pre-pandemic levels, it would take until 2033 to clear the backlog.
But if 15% more could be completed, backlogs could be cleared by next year.
Increasing activity levels would require more cash for new equipment and more staff, however.
And all this is dependent on those who have not come forward for checks seeking help.
Between March 2020 and February 2021, the number of referrals to see a specialist dropped by nearly 370,000 on the year before, a fall of 15%.
Behind these figures are thousands of people for whom it will now be too late to cure their cancer, the report, with the CF health consultancy, warns.
And it estimates the proportion of cancers diagnosed while they are still highly curable - classed as stage one and two - has fallen from 44% before to pandemic to 41%.
IPPR research fellow Dr Parth Patel said: "The pandemic has severely disrupted cancer services in England, undoing years of progress in improving cancer survival rates.
"Now, the health service faces an enormous backlog of care, that threatens to disrupt services for well over a decade.
"We know every delay poses risks to patients' chances of survival.
"Clearing the cancer care backlog before the next general election looks unlikely with the way the NHS is currently resourced, staffed and organised."