UK Health Secretary Jeremy Hunt announced an independent inquiry into the failings, attributed to a computer algorithm error. An estimated 450,000 women failed to get a letter inviting them to their final screening, he said.
In the UK, women between the ages of 50 and 70 are automatically invited for breast cancer screenings every three years as the likelihood of developing breast cancer increases with age.
In a statement to Parliament on Wednesday, Hunt said that an analysis by Public Health England found that women in England between the ages of 68 and 71 were not invited to their final breast cancer screening between 2009 and early 2018.
"At this stage it is unclear whether any delay in diagnosis will have resulted in any avoidable harm or death," he told Parliament.
Early indications suggested that between 135 and 270 women had their lives shortened as a result of the error, Hunt said.
"Tragically, there are likely to be some people in this group who would have been alive today if the failure had not happened," he said.
Health officials will contact the next of kin of women who are thought to have missed a scan and subsequently died of breast cancer, Hunt said. They will apologize and offer a process to establish whether the error led to an earlier death, and if compensation might be payable. "We recognize this will be incredibly distressing for some families," he said.
The independent review will be chaired by Lynda Thomas, chief executive of Macmillan Cancer Support, and Martin Gore, professor of cancer medicine at the Institute of Cancer Research and a consultant medical oncologist at the Royal Marsden Hospital.
A report is expected in six months, but measures have already been put into place to prevent further errors and to reassure those already affected.
The algorithm failure has been identified and fixed and the women affected -- of whom 309,000 are estimated still to be alive -- will receive invitations for screenings, Hunt said.
All women under 75 will automatically receive invitations to catch-up screenings and women 72 and over will be given access to a helpline to get clinical advice on whether a screening is appropriate for them.
"For older women there is a significant risk that screening will pick up nonthreatening cancers that may lead to unnecessary harmful tests and treatment; however, this is an individual choice," Hunt said.
All women affected will receive letters by the end of the month.
Responding to the announcement, Professor Helen Stokes-Lampard, chair of the Royal College of General Practitioners said: "We are shocked to learn that hundreds of thousands of women in England have missed out on their opportunity for breast screening."
"We welcome the independent inquiry into this matter, announced today, but the priority should not be to establish blame, but to put measures in place to invite those women affected for screening, where appropriate; to ensure there are enough resources in the system to cope with any additional demand that might follow as a result; and to take steps to ensure this never happens again."
NHS England will be expanding the capacity of screening services to enable all women affected to be screened within six months, though ideally as early as possible.
Breast Cancer Now Chief Executive Delyth Morgan welcomed the inquiry into what she called "a devastating error" for women whose cancer might have gone undetected. "It is beyond belief that this major mistake has been sustained for almost a decade and we need to know why this has been allowed to happen," Morgan said.
Shadow health secretary Jonathan Ashworth, of the opposition Labour Party, queried why it had taken so long for the error to be detected and asked for assurances that oversight of this and other screening programs would be improved.
According to Public Health England, the screening program in England detects about 18,400 cancers per year, saving 1,300 lives.
Health officials in Wales and Northern Ireland, which use a similar IT system, do not believe their