Health and Social Care Secretary Jeremy Hunt told MPs that a "serious failure" in the screening programme meant an estimated 450,000 women aged between 68 and 71 were not invited for their final mammogram between 2009 and 2018.
It is not known whether any delay in diagnosis resulted in avoidable death, but it is estimated that between 135 and 270 women had their lives shortened as a result, he said.
Breast Cancer Now said it is "beyond belief" that the "colossal systematic failure" occurred for almost a decade.
The charity urged anyone who is concerned that they may have missed their screening to contact the Public Health England helpline on 0800 169 2692.
Meanwhile, the Royal College of GPs called for action to "ensure this never happens again".
"We are deeply saddened and extremely concerned to hear that so many women have been let down by such a colossal systematic failure," said Baroness Delyth Morgan, chief executive at the charity Breast Cancer Now.
"That hundreds of thousands of women have not received the screening invitations they've been relying upon, at a time when they may be most at risk of breast cancer, is totally unacceptable.
"We know this will unfortunately be incredibly difficult news for many women to hear.
"Public Health England will be directly contacting all women affected - we'd urge against panic and encourage anyone concerned that they have missed their screening invitations to contact the Public Health England helpline directly for further advice.
"Screening prevents deaths from breast cancer - the earlier the disease is detected, the more likely treatment is to be successful, and we'd encourage all women to attend their appointments.
"For those women who will have gone on to develop breast cancers that could have been picked up earlier through screening, this is a devastating error.
"It is right that Public Health England are offering the option of catch-up screening for those affected, and hope that women will choose to take this up.
"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. We welcome the independent inquiry to ensure this can never be repeated."
Samia al Qadhi, chief executive of charity Breast Cancer Care, said: "Hundreds of thousands of women across England have been failed by this appalling error and some have had their lives shortened as a result.
"It is shocking that almost a decade has passed before this mistake was discovered.
"Women affected and their loved ones will be left reeling, both scared and confused. The number one priority now must be to ensure that they get all the support and information they need.
"This incompetence must not be allowed to happen again."
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.
"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."
Professor Helen Stokes-Lampard, chairwoman of the Royal College of GPs, said: "The national breast screening programme has potentially saved thousands of lives since its inception - last year alone, over 18,000 cancers were detected as a result of the programme, which might not have been detected as early otherwise.
"We are shocked to learn that hundreds of thousands of women in England have missed out on their opportunity for breast screening - and the implications for GPs and our teams will potentially be significant, as patients seek reassurance and to find out where they go from here.
"We welcome the independent inquiry into this matter, 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."