Health secretary Andy Burnham said he deeply regrets the distress caused to grieving families as it emerged around 800,000 people had their wishes about the use of their organs wrongly recorded due to an error.
An investigation found that 45 people for whom false data was stored have since died.
The NHS is about to contact approximately 20 families who allowed organs to be taken after being misinformed about what consent had previously been given.
Mr Burnham said: “I have asked NHS Blood and Transplant to take immediate steps to identify and contact all affected families. This process is under way and will be completed as quickly as possible.
“I have asked Professor Sir Gordon Duff of Sheffield University to carry out a review to find out why this has happened, prevent mistakes like this being made again and ensure all necessary steps are taken to maintain confidence in the organ donor register.”
The mistake came to light last year when NHS Blood and Transplant wrote letters to new donors thanking them for joining the register, and outlining what they had agreed to donate.
Some of them wrote back complaining that the information was wrong.
In the cases where errors were made, families are believed to have been asked for permission, but their decisions were based on misinformation about the wishes of their relatives.
A spokeswoman for NHS Blood and Transplant said: “We have identified a technical error in recording information on the NHS Organ Donor Register. This only affects those who have registered via the driving licence application form.
“We are still checking our records to ensure that other donors or families have not been similarly affected.
“We sincerely apologise for any distress this may have caused. We can reassure everyone that no organs have been donated without the support of the deceased’s nearest relatives and that no one has been registered as a donor against their wishes.”