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.
He admitted 450,000 women could be affected, and that between 135 and 270 women could have had their lives shortened as a result.
Baroness Delyth Morgan, chief executive at Breast Cancer Now, said it was a "colossal systemic failure".
Widower Brian Gough said his wife Trixie never received a letter inviting her to go for a screening in 2009 - and that a scan in October 2010 revealed she had stage-three breast cancer.
The 77-year-old from Norfolk told the Press Association he was watching the television on Wednesday when the news of the screening error broke, leaving him "shell shocked".
"There has always got to be some blame these things don't just happen ... it is never the computer that goes wrong it is the person that put the information in or took it out," he said.
"Somebody somewhere along the line has made a massive error - we are talking 450,000 letters that should have gone out."
On Wednesday Mr Hunt said "administrative incompetence" meant some families may have lost, or may be about to lose, a loved one to cancer.
Women in England between the ages of 50 and 70 are currently automatically invited for breast cancer screening every three years.
The issue was first brought to the attention of the Department of Health and Social Care in January, but was initially thought to pose a "limited" risk to patients.
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.
Despite his shock, Mr Gough said he admired the Health Secretary for "getting up and not trying to hide the truth".
"I am glad the truth has come out, and I just hope that people take more notice of these glitches," he said.
"Potentially we are talking about 450,000 women who could have died, it is all very well saying only a percentage but we are not born as a percentage of anything, we are a person.
"And those people have got families, friends and lives to lead, and they have been cut short."
He said his wife of 56 years died three days after Christmas in 2015, and that the 76-year-old never once complained during her cancer ordeal.
Mr Gough said she missed the wedding of her grandson as she was too ill to attend, and died just before her granddaughter's nuptials.
"All of that she missed because she didn't get diagnosed and she didn't know anything about it until a year too late," he said.
Baroness Morgan said Breast Cancer Now welcomed the inquiry to ensure similar mistakes cannot be made.
She said: "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 are deeply saddened and extremely concerned to hear that so many women have been let down by such a colossal systemic failure.
"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."
Patricia Minchin, 75, said she was not offered a screening in 2013 when she turned 70, and is battling breast cancer.
The cancer has also spread to other parts of her body.
The grandmother and mother-of-four from Bushey, Hertfordshire told the Telegraph: "I feel so disappointed. I don't know if I'm going to survive.
"I would like an explanation from somebody why this happened, why I didn't get a recall.
"Why didn't they pick up that I hadn't had a mammogram? They obviously knew about it for some time and they shouldn't have covered it up for so long.
"I feel absolutely let down. I worked for the National Health Service all my life, I was a nurse."
Of those who missed invitations, 309,000 are estimated to still be alive and all those living in the UK who are registered with a GP will be contacted before the end of May.
All women who were not sent an invitation for their final screening will be given the opportunity to have a new appointment.
Those under the age of 72 will receive an appointment letter informing them of the time and date, while those over 72 will also be offered a screening and have access to a helpline to decide if it will be beneficial.
The helpline for those who think they may be affected is 0800 169 2692.
Dr Jenny Harries, deputy medical director of Public Health England, told BBC Radio 4's Today programme: "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.
"We have a screening programme that is world-class. It affects all of us. Breast cancer affects one in eight women and many of our organisation members, of course, use the service just like other members of the public.
"We wouldn't want any lives to be shortened. We have gone back and fixed all these glitches and audited that, so women can be assured going forward that that is sorted."