The news will come as a blow to subpostmasters and campaigners who have fought to save the card with the help of a petition signed by more than one million customers.
The National Federation of Subpostmasters (NFSP) has warned of further closures if the government does not establish a post office-based replacement for the card.
Government ministers have claimed that pilot schemes to test a variety of ways customers collect their benefits and pensions showed that an overwhelming majority will accept having all of their payments made into their bank account. But opposition MPs have argued that the government is relying on research among people who were forced to switch from card accounts, rather than listening to those who signed the petition.
NFSP general secretary Colin Baker told Convenience Store: "If a post office-based solution to replace the card is not found, then there is no doubt there will be closures. We do seem to be making a bit of progress, however, and I'm more hopeful than I was in January when all that ministers wanted to do was scrap the card account without thinking of a replacement.
"The petition and an Early Day Motion, signed by a record number of MPs, have helped and the effort over the summer has forced a cross-party look at the Post Office. There isn't one solution. There needs to be different solutions to cater for a number of different customers."
Judy Bloomfield, subpostmaster at Plymtree Post Office Stores in Devon, believes the card account is a lifeline for many of her customers. She said: "I feel strongly that it should not be abolished. We are five miles from the nearest large town and there is no regular bus. The shop is the hub of the village and customers rely on us. With the TV licence payments already gone, to lose the card account would be yet another blow. We need more transactions, not fewer."
Mark Bamforth, subpostmaster at Lytham St Annes, Lancashire, added: "Bank branches are disappearing all the time and a huge number of pensioners rely on being able to use the card account here. It brings in a lot of business and would be devastating if it was scrapped."