Health Secretary Jeremy Hunt has launched an independent enquiry into breast cancer screening, after 450,000 women were reportedly not invited for screening by the NHS.
Of these, 150,000 have died since and the remaining 300,000 are aged in their 70s, the BBC said.
Mr Hunt said that a "serious failure" had come to light in the national breast screening programme in England, overseen by Public Health England (PHE).
He said: "Earlier this year PHE analysis of trial data from the service found that there was a computer algorithm failure dating back to 2009.
"The latest estimates I have received from PHE is that as a result of this, between 2009 and the start of 2018, an estimated 450,000 women aged between 68 and 71 were not invited to their final breast screening.
"At this stage it is not clear whether any delay in diagnosis resulted in any avoidable harm or death and that is one of the reasons I am ordering an independent review to establish the clinical impact.”
The issue was first raised by PHE to the Department of Health and Social Care but was not “escalated to ministers” until March, Hunt said, "with clear clinical advice that the matter should not be made public".
Addressing Commons earlier today, he admitted that the failure to be invited for screening may have left some women with cancer.
“Many families will be deeply disturbed by these revelations, not least because there will be some people who receive a letter having had a recent diagnosis of breast cancer,” he said in his opening statement.
“We must also recognise that there may be some who receive a letter having had a recent terminal diagnosis.
“For them and others it is incredibly upsetting to know that you did not receive an invitation for screening at the correct time and totally devastating to hear you may have lost or be about to lose a loved one because of administrative incompetence.
“So on behalf of the government, Public Health England and the NHS, I apologise wholeheartedly and unreservedly for the suffering caused.
Emma Greenwood, Cancer Research UK's director of policy and public affairs, said: "It's very concerning to learn that so many women have not received an invitation to screening over a prolonged period of time.
"We know this may leave many women with questions about breast screening.
“If you suspect you have been directly affected by this or if you are over 50 and haven't had a mammogram in the last three years and would like one, the NHS Choices website provides further information and the option to contact your local unit to book an appointment.
"It's worth remembering that many breast cancers are still found by women themselves, outside of the screening programme, so if you notice any unusual changes in your breast, see your GP straight away."
Mr Hunt continued: "Our current best estimate which comes with caveats as it's based on statistical modelling rather than patient reviews, and because there is currently no clinical consensus about the benefits of screening for this age group, is that there may be between 135 and 270 women who had their lives shortened as a result.
"I am advised that it is unlikely to be more than this range and may be considerably less.
"However, tragically there are likely to be some people in this group who would have been alive today if the failure had not happened."