A study in 2012 estimated that women who attend breast cancer screenings are 20% less likely to die of breast cancer than those who don't. A scan in October 2010 revealed she had stage-three breast cancer.
The helpline for those who think they may be affected is 0800 169 2692.
It is not as simple as finding someone who was not sent a screening letter and subsequently died from the disease.
Jeremy Hunt, the Health Secretary, has admitted as many as 270 women may have died early as a result as they were never invited to their final check-up.
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. She was registered with a GP but had not had a mammogram for several years.
"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".
Baroness Delyth Morgan, chief executive at Breast Cancer Now, said the error was a "colossal systemic failure".
And in a statement released on Thursday night, Mr Selbie said: "On behalf of PHE and NHS breast screening services, our apology is heartfelt and unreserved".
"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".
The "serious failure" in the code governing the NHS's national breast screening programme occurred in 2009, but only came to light when Public Health England (PHE) analysed the service earlier this year.
Because of a glitch in the algorithm, many women around the age of 70 did not get an invitation for their final screening. This is important: some of the women affected will be nearly 80 years old and, depending on their general health, there is a risk they could undergo treatment for lesions that would be so slow-growing they would never have caused any problems.
"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.
"Breast cancer screening has both harms and benefits and so, if some people have not been invited for screening they will have avoided the harms as well as missing out on any benefits".
"We must also recognise that there may be some who receive a letter having had a recent terminal diagnosis". Some women with screen-diagnosed breast cancer will have unnecessary mastectomies, and some will have unnecessary radiotherapy.
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.