The British government said it would guarantee all deposits with the Northern Rock bank.
The pledge by Chancellor Alistair Darling is an attempt to reinforce confidence in the beleaguered bank.
More than £2bn, around 8% of the bank's deposits, has been withdrawn by customers since the bank applied for an emergency loan from the Bank of England last week.
In Dublin, up to 300 customers queued at the Dublin branch of of Northern Rock, anxious to withdraw their savings.
Many online customers were unable to access their funds as the website came under pressure due to increased traffic.
The bank's shares were down 40% at one point on today and ended 35.4% lower as fears grow for its future. The bank is now likely to be sold off.
Queues started forming in the early hours of this morning, with some customers arriving as early as 3am in the UK.
Northern Rock, which is Britain's fifth-biggest mortgage lender, has said there is no need for investors or customers to panic and insisted it remained solvent.
It has about 25,000 clients in Ireland who hold around €2.3bn at the bank.
The Irish Financial Services Regulatory Authority is providing advice on 1890 777777. It says Irish consumers' savings are covered by the UK deposit protection scheme.
