Around one in eight women in the UK are diagnosed with the disease during their lifetime, according to the health service.
Hunt told the Commons that he had been made aware of a "serious failure" in the national Breast Screening Programme in England.
He said: "The latest estimates I have received from PHE is that, as a result of this between 2009 and the start of 2018, an estimated 450,000 women aged between 68 and 71 were not invited to their final breast screening.
"At this stage, it is unclear whether any delay in diagnosis will have resulted in any avoidable harm or death, and that is one of the reasons I am ordering an independent review to establish the clinical impact."
Hunt told MPs that estimates suggest "there may be between 135 and 270 women who have had their lives shortened as a result. I am advised it is unlikely to be more than this range and may be considerably less."
"However, tragically, there are likely to be some people in this group who would have been alive today if the failure had not happened," he added.
Among the 309,000 women being contacted, some will have been recently diagnosed with breast cancer, including terminal cases, he said.
Hunt said he was commissioning an "independent review of the NHS breast screening programme" to look at issues including its processes, IT systems and further changes and improvements "to minimise the risk of any repetition".
The review, expected to report in six months, will be chaired by Lynda Thomas, the chief executive of Macmillan Cancer Support, and leading oncologist Professor Martin Gore.