Hunt told the House of Commons that because of a computer algorithm failure an estimated 450,000 women aged between 68 and 71 were not invited to their final breast screening between 2009 and the start of 2018.
"Since 2009, in Northern Ireland women become eligible to be invited for breast screening every three years from the calendar year they turn 50 to the calendar year they turn 70".
Hunt said he was "not aware of any evaluations that have been shared with the Department of Health that could have brought this problem to light", but said the inquiry would look at the matter.
"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".
"We would like to reassure women in Wales that we believe this issue to be one that predominantly affects England".
Some people will receive a letter stating they missed out, knowing they now are terminal ill.
Of these, 150,000 have died since and the remaining 300,000 are aged in their 70s, the BBC said.
Some of the women affected have since gone on to develop breast cancer. Hunt said that this highlighted that some women on the AgeX trial were not receiving an invitation to their final screening as a 70 year old.
It has emerged 450,000 women were not invited to appointments as they should have been, and as a result up to 270 maybe have "had their lives shortened", according to the BBC.
At the time of the discovery, Hunt said, Public Health England advised him that the public should not be told to allow time for remedial measures to be put in place.
It said, "The fault has now been identified and fixed and women who did not receive their final routine invitation and are registered with a GP are being contacted and offered the opportunity to have a catch up screen".
That system is supported by three sub-systems: Breast Screening Select, Breast Screening Information System and the National Breast Screening System.
GPs' leaders said they were "shocked" to learn of the error and said the implications for Global Positioning System would potentially be "significant".
"I am glad the truth has come out, and I just hope that people take more notice of these glitches, it really does affect people's real lives, devastatingly, it really devastates".
It's thought one in eight women and one in 870 men will be diagnosed with breast cancer in their lifetime.