More than 2,000 new claims for compensation were filed last month by people who also believe they are victims of the Post Office scandal, a government minister said.
Postmaster General Gareth Thomas told BBC Newsnight that the new claims came after the Post Office contacted former sub-postmasters who may have been affected but had not yet claimed compensation.
Many of the more than 4,000 original claimants are still waiting for compensation to be paid to them, including Betty Brown, 92, who told the BBC the government must “get this done”.
Thomas said the compensation process was getting faster and becoming “less legalistic, less adversarial.”
Ms Brown told the program on Monday that she had so far been offered less than a third of what she had asked for in compensation.
“We have waited and waited. Time is getting shorter. We are getting older,” she said. “Do it.”
She added that she wanted a “fair and equitable hearing.”
Mrs Brown and her husband spent more than £50,000 of their savings to cover money which appeared to be missing from their County Durham branch due to faulty Horizon software.
She was forced out of her job and forced to sell her post office at a knockdown price in 2003.
Thomas said he was “keen to find solutions” and would meet with her and another former deputy postmaster, Shazia Saddiq, who told Newsnight she was only offered 10 per cent. of his claim.
Ms Saddiq ran three post offices in Newcastle-upon-Tyne, but “lost everything” and had to leave the area where she lived after being attacked in the street.
The former subpostmasters spoke to Newsnight a year after an ITV drama highlighted the scandal.
Earlier this month, Parliament’s Business and Commerce Select Committee called for changes to the way compensation was paid, due to persistent delays.
Thomas said he was “happy to say” that more victims were coming forward and the government was looking at ways to speed up reparations.
He said the amount of compensation paid had doubled in the last six months and the government was trying to make compensation systems “less legalistic, less contradictory”.
Claimants can choose to receive a fixed compensation of £75,000 and avoid a lengthy assessment process, which should allow claims to be processed more quickly, it added.