The Post Office has offered compensation to 777 of the 2,500 postmasters who applied for compensation over a 20-year scandal that saw some of them serve prison sentences.
Its chief executive, Nick Read, told MPs on Tuesday that he hopes that lawyers and staff working on the case can make offers to the all but a handful of the claimants by the end of the year.
But he warned that the Post Office will need help from the Government to ensure that all the postmasters are properly compensated for what happened to them.
“The Post Office itself doesn’t have the financial resources to compensate a miscarriage of justice of this scale,” he told the Business, Energy and Industrial Strategy Committee.
In total, 950 postmasters were prosecuted for a variety of charges from 1999, but many of these cases were later linked to problems in the Horizon computer system.
Some of the postmasters were sent to prison for false accounting and theft. So far, 72 convictions have been overturned.
Mr Read said that 66 of those people who have seen their convictions overturned have applied for an interim £100,000 payment designed to “bridge the gap” until a full settlement can be reached, Mr Read said.
The Post Office has paid out interim payments to 57 of these.
“As soon as (convictions) have been overturned … the Post Office will be paying those interim payments within 28 days,” said business minister Paul Scully.
But the Post Office is yet to be able to contact 127 of the 736 former postmasters whose convictions were linked to Horizon.
“It is my intention that we do give full and final compensation of all the victims of the past and their families,” Mr Read said.
He added: “There is an enormous amount of complexity associated with making sure we get absolutely right how we compensate those postmasters.
“And most importantly that it’s full, it’s fair and it’s final.”