Blackbird Leys in Oxford has been snubbed by the Royal Bank of Scotland which had promised to roll out free-to-use cash machines to deprived areas.
The only cash machine on the estate at the moment charges customers £1.75 for each withdrawal.
Residents, backed by their MP Andrew Smith, had hoped to be included in the bank's scheme to install 300 free-to-use machines across England in areas where residents have no free access to their cash.
But RBS has now ruled out any chance of helping the estate's 12,000 residents, because there is another free-to-use cash machine within one kilometre.
However, there is still a chance one of the non-charging cash machines could be put in Rose Hill and Barton.
The free cash machine plan was devised after East Oxford MP Mr Smith, who lives in Blackbird Leys, brought the issue up in the House of Commons.
Mr Smith has now been invited to meet the bank's bosses to persuade them to change their minds.
He said: "I'm determined to get the free cash machines for Blackbird Leys, Barton and other estates.
"It's not good that RBS is getting loads of publicity by saying they want to do something like this and then setting the bar so high areas cannot meet the rigid criteria.
"I've been offered a meeting with RBS and I will be making the case for Oxford estates in no uncertain terms. I will be raising the concern again in the House of Commons if the answer is insufficient."
RBS launched the scheme last month asking residents who have no access to a free cash machine to nominate their area.
Blackbird Leys and Greater Leys has one cash machine in Blackbird Leys Road which charges every time one of the estate's 12,000 residents uses their cash card.
The bank received three nominations for Blackbird Leys and Greater Leys.
Jim Hewitt, treasurer of the Blackbird Leys Credit Union, said: "Ultimately no area in the country should be at a disadvantage.
"It is the Government's responsibility to make sure everyone has adequate access to cash.
"If you wrote down four fundamental things a Government has to do - making sure people have access to their money would be one of them."
A spokesman for the Royal Bank of Scotland said: "Unfortunately Blackbird Leys does not qualify because it is within one kilometre of our machines, which are in Boots and Tesco in Cowley nearby.
"It doesn't meet our criteria.
"We have got to be quite strict about this."
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