Abbey branches are now able to process applications on the spot
Fifteen thousand applicants for Abbey's postal cash ISA have been left not knowing whether their form has even been received.
When the ISA was launched a month ago it proved extremely popular, and from 1 June it is offering an attractive interest rate of 4.85%.
But thousands who rushed to take advantage of the offer have now been waiting for up to a month without hearing anything back from the bank.
Abbey told the programme it had been overwhelmed with applications but was "trying to apply every ounce of resource" into clearing the backlog.
BBC Radio 4's Money Box has heard from a number of applicants who have been left frustrated and confused by the process.
Keith from London told the programme: "It is difficult to know what to do. Stop the cheque? Perhaps reapply, or just forget about the whole thing."
Money Box spoke to Abbey's Director of Savings and Investment Paul Masters about the problem.
He said: "This is an example of a problem caused by the account being even more successful than we expected it to be.
"I absolutely apologise to all of the customers who have experienced delays and in particular for any stress that they have experienced."
In response, Abbey have increased the number of staff handling the applications but were unable to say when the backlog will be cleared.
BBC Radio 4's Money Box was broadcast on Saturday, 15 May, 2004 at 1204 BST.
Mr Masters told the programme: "We will clear them absolutely as fast as we possibly can... We are trying to apply every ounce of resource that we can, to do this quickly."
He added that all of those stuck in the processing backlog would receive a letter to at least let them know that their application had been received.
And he was keen to point out all applications are date-stamped on receipt, and the interest accruing on the account will be backdated to that date.
Although the Abbey website says you cannot open a postal account in a branch. You can now.
For those wishing avoid the delays, all Abbey branches are now able to do on-the-spot processing of applications.
BBC Radio 4's Money Box was broadcast on Saturday, 15 May, 2004, at 1204 BST.
The programme was repeated on Sunday, 16 May 2004, at 2102 BST.