The independent review of the NHS breast screening programme will be chaired by Lynda Thomas, chief executive of Macmillan Cancer Support and Professor Martin Gore, consultant medical oncologist and professor of cancer medicine at The Royal Marsden.
The fault has now been identified and fixed, and women who did not receive their final routine invitation are being contacted and offered the opportunity to have a catch up screen.
Mr Hunt said "administrative incompetence" meant some families may have lost, or be about to lose, a loved one to cancer.
The errors are due to a computer problem, which meant that many women did not receive their final invitation to attend breast screening appointments, usually offered between the ages of 68 and 71.
Breast Cancer Care said its helpline had received four times its usual number of calls in one day.
Despite his shock, Mr Gough said he admired the Health Secretary for "getting up and not trying to hide the truth".
The IT error took place in 2009 but only came to light in January this year, Hunt said.
Of the 450,000 women affected, 150,000 had died.
Patricia Minchin said her "traumatic journey" could have been "avoided".
"I'm angry, we won't know if it would have lengthened her life of saved or life - but we will always wonder now", she said.
"Financial hardship plays a role in delays, discontinuation and omission of treatment, and thus may correlate with racial disparities in breast cancer death", said UNC Lineberger's Stephanie Wheeler, the study's lead author and an associate professor in the UNC Gillings School of Global Public Health. "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", Morgan said.
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"We are deeply saddened and extremely concerned to hear that so many women have been let down by such a colossal systemic failure".
Nearly 300 women may have died in the United Kingdom because they missed out on breast cancer screenings due to a computer error.
The women who have been affected by the breast cancer screening failure will be contacted.
She said: "You can never say it could have been prevented but I really think if I had had a mammogram when I was 70, (the cancer) may have been picked up". On average, black women in the analysis were slightly younger, and they presented with higher-stage disease at the time of diagnosis.
"I feel absolutely let down".
The National Health Service could now face a massive compensation bill.
Around 309,000 women 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.
Letters will be sent out women to notify them of missed screenings over the next few months.
All women under 75 will automatically receive invitations to catch-up screenings and women 72 and over will be given access to a helpline to get clinical advice on whether a screening is appropriate for them.
"I don't know about whether she could have been saved, but I think she would have lived longer", he told The Telegraph.
"We have a screening programme that is world-class". It affects all of us.