By Louise Greenwood
BBC Radio 4's Money Box
The HiSave account has to be opened and run online
ICICI UK has admitted it struggled to cope with a flood of applications for its market-beating savings account, but claims the backlog is now cleared.
The bank was offering 5.4% interest on its internet based HiSave account.
That rate will be cut from 1 November to 5.15%, but the bank still promises to pay 0.25% above the Bank of England base rate until December 2007.
Owned by India's second largest bank, ICICI UK claims it can offer this rate because it has low running costs.
However, BBC Radio 4's Money Box programme has been contacted by a number of people who have encountered problems when trying to open an account.
Dave from Exeter gave up after twice trying to apply online.
"I'll wait until I see some evidence that they've actually got their act together," he said.
"Once it seems likely that they can offer a decent service then I'll probably apply again for a third time and see what happens."
Money Box has also spoken to listeners who had sent off cheques which were cashed
but months later were still waiting to receive their account details, with no idea where their money was.
Peter from West London, sent a cheque for £500 in July.
Eight weeks later, having e-mailed and rung ICICI UK Customer Services, he finally called the head office in Knightsbridge and demanded his money back.
Chief Executive of ICICI UK, Sonjoy Chaterjee, explained what had gone wrong: "Clearly there was a huge avalanche of applications.
"Unfortunately, the pace at which those people came was well beyond our expectations."
And he assured the programme the problems had been resolved.
"In terms of where we are today... We have nothing pending on our processes... So today if you were to make an application on our website you would get a response back in two days that your account is opened."
But he stopped short of making that a promise, saying: "I wouldn't call it a promise, it's a service we hope we are delivering at this juncture.
"I know there have been issues in the past but today we hope to deliver on these service parameters."
Meanwhile, customers have been assured that any interest due will be backdated from the point where their cheque was cleared.
BBC Radio 4's Money Box was broadcast on Saturday,1 October, 2005, at 1204 BST.
The programme was repeated on Sunday, 2 October, 2005, at 2102 BST.