Up to 75 women may have died early following blunders in a breast screening, according to latest estimates.
NHS records show as many as 174,000 women were affected by failures in the programme and 130,000 are still alive.
Between 135 and 270 were feared to have had their lives cut short as a result of the mistake, Jeremy Hunt had warned when he revealed the problem in May.
But the figure has been revised down to fewer than 75, the Health Secretary announced in a written statement to parliament.
It is now clear that this may have resulted in significant harm for a small number of women, while thousands more have faced unnecessary distress and anxiety as they waited to hear if they have been affectedJeremy Hunt
“Whilst this figure is lower than the original estimates given in my statement, this does not lessen the devastating impact that this has had on some people’s lives,” Mr Hunt added.
Computer system failures meant thousands of women aged 68 to 71 were not invited to their final routine screening between 2009 and May 2018.
Public Health England contacted 195,565 women registered with a GP in England by the end of May who had missed their screening.
All the affected women known to have moved to other parts of the UK – 503 women in Scotland, 94 women in Wales and 72 women in Northern Ireland – were also written to.
Overall, nearly 27,000 have now received an appointment for screening.
An emergency helpline set up to speak to women concerned they had been affected has received 46,000 calls.
All those affected who want to be screened will be seen by the end of October, Mr Hunt said.
Screening is a procedure that allows doctors to catch breast cancer while it is still in its infancy and therefore easier to treat.
It involves an X-ray test – known as a mammogram – to check for signs of cancer which are too small to see or feel.
A “failure” stretching back to 2009 with a computer algorithm meant invitations were not sent to all those who should have received them.
Mr Hunt said: “Our cancer screening programme is widely recognised as world-leading, but on this occasion a number of women have been let down.
“It is now clear that this may have resulted in significant harm for a small number of women, while thousands more have faced unnecessary distress and anxiety as they waited to hear if they have been affected.
“I would like to repeat my wholehearted and unreserved apology to the women affected and their families – and above all reassure them that we are working hard to understand what went wrong and what we need to do to stop similar incidents from happening in the future.”
Public Health England chief executive Duncan Selbie said: “Our priority throughout has been the wellbeing of affected women and giving them the support they need.
“I would like to reiterate our heartfelt and unreserved apology that this has happened. We welcome the terms of reference of the independent review and we will work fully with them to ensure it cannot happen again.”