Health Secretary Jeremy Hunt has launched an independent review after he revealed a computer error dating back to 2009 meant many women aged 68 to 71 in England were not invited to their final routine screening.
But he added: 'However tragically there are likely to be some people in this group who would have been alive today if the failure had not happened'. They should receive a letter from their GP about the test, which aims to catch cancer early when it is easier to treat.
Brian Gough, whose wife Trixie died of breast cancer aged 76 in 2015, said she was among the women not invited for a scan.
Hunt has now ordered an independent review into the programme, which will include examining the processes and IT systems in place.
Jeremy Hunt, speaking in the Commons yesterday, stated that an estimated 450,000 women between ages 68 and 71 did not receive invitations to the screening due to a computer algorithm error since 2009.
It is thought that an IT error made in 2009 is responsible for the situation that, it is now estimated, led to the death of 270 women.
"It's worth remembering that most 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 said all women affected would be contacted by letter by the end of May and those under 72 would receive an appointment for a catch-up mammogram.
Women in Scotland are not affected by the error because it has a different IT system.
"Unfortunately, we don't know why patients were more likely to obtain future cancer screenings over the longer term, which is why we need more research".
The current NHS leaflet states that, for every 200 women attending screening between the ages of 50 and 70, we would expect one to have her early death from breast cancer prevented, but three to be unnecessarily treated for a harmless cancer that would not have troubled them.
An upgrade to the invitation IT system provided improved data to local services which led to the problem being identified.
"Employer-sponsored health insurance and paid sick leave are often reserved for employees with higher earnings, full-time status, and more generous benefits, which may correlate also with race", she said. It is hard to imagine what some of the worst affected families will be going through over the next few weeks.
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".
Women who are concerned about whether they had missed a screening can call 0800 169 2692.
Dr Jenny Harries, deputy medical director of PHE, said: "There are a number of organisations involved in this and I think we are all - Public Health England, the NHS, NHS Digital, the Department of Health - devastated by this".