Of those who missed invitations, 309,000 are estimated to still be alive and all those living in the United Kingdom who are registered with a GP will be contacted before the end of May.
Call the breast screening helpline number 0800 169 2692 for more information, or visit the NHS Choices website.
But it means that up to 800 women may have been saved from harm by not sending them their final screening appointment letter, as they avoided possible reduction in their life expectancy through unnecessary treatment.
Health Secretary Jeremy Hunt apologized in parliament for the "serious failure", which he said was the result of a mistake in a computer system's algorithm dating back to 2009 but identified only in January this year.
Under the United Kingdom health system, Patricia Minchin was due to have a mammogram five years ago after she turned 70, but the notification never arrived.
"Can I ask the Secretary of State what conversations he's had with the Welsh Secretary because having long since passed the ages he mentioned, I certainly was never invited for a screening, I had to ask for one and eventually got the screening in England".
This is because the likelihood of getting breast cancer increases with age.
Baroness Delyth Morgan, chief executive at Breast Cancer Now, said it was a "colossal systemic failure".
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Mr Hunt said: "Irrespective of when the incident started, the fact is that for many years oversight of our screening programme has not been good enough".
The error remained undetected for eight years until Public Health England - which oversaw the program - discovered the problem after it began analysing data from the screenings. It was escalated to ministers in March by PHE following an urgent clinical review, with the Government told the error should not be made public to ensure existing screening services were not overwhelmed.
England's breast-screening failure follows unrelated news in Ireland last week that more than 200 cervical cancer test results should have resulted in earlier intervention.
"It is beyond belief that this major mistake has been sustained for nearly a decade and we need to know why this has been allowed to happen", said Delyth Morgan, chief executive of Breast Cancer Now. This problem has affected thousands of women over many years.
Yorkshire Cancer Research said three in 10 breast cancers were found through screening and 85 per cent found by screening were diagnosed at an early stage.
Mammograms are now the best-available tool for detecting breast cancer early and are linked to a reduction in deaths from the disease, although not a large one.
The breast cancer screening aims to spot cancer early, by using an X-ray mammogram to detect tumours that are too small for us to spot ourselves.