Icesave customers can soon trigger the process to get their money back
The 230,000 UK savers in the collapsed Icesave internet bank are being sent e-mails this week telling them how they can get their money back.
The bank closed at the beginning of October when its parent company, Iceland's Landsbanki, went bust and was then nationalised.
The process should see the first deposits start moving into customers' alternative bank accounts next week.
The UK government has promised that UK savers will get all their money back.
Meanwhile, thousands of people who had put money into the Isle of Man arm of Iceland's biggest bank, Kaupthing, are still in limbo.
Icesave customers will receive two e-mails from the Financial Services Compensation Scheme (FSCS).
The first will tell them that the process for retrieving their money is being launched, and the second will then give them precise details of what they should do.
"They will be asked to go onto the existing Icesave UK website, using their existing logins," an FSCS spokeswoman explained.
"They will be given a time from when they can log in and move their money," she added.
The process will be purely online, with customers being given a month to move their cash.
"If they have not done this within a month there will be a paper application process, and we will contact them if they haven't logged on to complete their payments," the FSCS spokeswoman said.
The customers, who have about £4.5bn between them, should receive their cash in their accounts within five days of triggering the payment.
Under the terms of the compensation limits that were increased at the start of October, the FSCS will pay 100% of the first £50,000 of any depositors money that is at risk from a bank being declared insolvent.
However, because of the prospect of many savers losing much more, the government decided to repeat the promise it made to Northern Rock savers last year when that bank was on the verge of collapse, and said it would top up the FSCS so that it could pay out all the savings that were at risk in Icesave.
In theory, the first tranche of each individual's savings, about £16,300, should have been paid by the Icelandic depositors protection scheme, but the UK chancellor Alistair Darling pointed out at the time that it did not appear to have any money in it.
Savers who have money in an Icesave Isa will be able to move their investments to a new Isa with an alterative financial institution, without losing the Isa's favourable tax status.
Kaupthing Isle of Man
Meanwhile, thousands of savers with money in the Isle of Man arm of Iceland's Kaupthing Singer & Friedlander, KSF-IOM, will have to wait at least until 27 November to find out whether they will get any money back.
The Manx High Court may decide then to wind it up.
The Isle of Man bank was put into provisional liquidation in October when its parent company was taken over by the Icelandic authorities to stop it collapsing.
At the same time, UK authorities froze all Kaupthing's assets in the UK.
The Manx operation has 7,000 accounts, holding £850m, most of which belongs to people living outside the island.
Under the recently revamped rules of the IOM's Financial Supervision Commission, depositors will eventually be able to reclaim up to £50,000, if the bank is declared to be insolvent.
This is regardless of where they live.
On Monday the UK chancellor, Alistair Darling, said he would not underwrite any savings held in KSF-IOM, a move which might have offered them hope of a greater level of compensation.
"They [Manx banks] are regulated by the Isle of Man authorities, and I would have to think long and hard before saying, for the first time, the British Government would then go and underwrite savings made in another jurisdiction," he told the UK's Treasury Select Committee.
Last month he arranged for the Dutch bank ING Direct to take over the accounts of 160,000 people who had money saved with KSF in the UK, and the accounts of 22,200 people who held accounts with the Heritable bank, a subsidiary of Landsbanki.