"The self-imposed framework is designed to ensure Northern Rock does not take unfair advantage of government support during the period of temporary public ownership," a spokesman said.
When it was nationalised, Northern Rock said it would limit its share of retail deposit balances to 1.5% of the market in the UK and 0.8% in Ireland. Its share of gross new mortgage loans would also be no more than 2.5% of the UK market, it said.
A number of media commentators advised savers to turn to Northern Rock at the weekend. Northern Rock does not advertise its 100% guarantee.
One customer who has decided to move around his savings is retired accountant David Roots, from Somerset.
The 43-year-old had £102,000 saved with ING, £52,000 with Bradford & Bingley and £21,000 in an Isa with Alliance and Leicester.
He has decided to keep £35,000 with B&B and A&L owner Santander, another protected £35,000 with ING and the remaining £105,000 with the fully protected Anglo Irish Bank.
"I know it is selfish but I am concerned about what is happening," he said.
"If people move money around then it might destabilise the banking sector, but you have to act for yourself."
He called for the UK government to protect 100% of savings, and for more regulation to prevent banks lending beyond their means.
He is one of relatively few people who have more than £35,000 saved in one account.
Figures from the British Bankers' Association published last year suggest that 4% of the 150 million deposit accounts in the UK had funds in excess of the current guaranteed safety threshold of £35,000.
Some 2% of these contained funds in excess of £50,000.
However, these figures pre-date much of the banking crisis and it is highly likely that many of these savers have since spread these funds among various accounts.
Small businesses are also covered under the UK scheme for the first £35,000 of deposits.
They must satisfy two of the following three criteria: a turnover of not more than £6.5m, a balance sheet total of not more than £3.26m and a total number of employees of not more than 50.
Larger businesses are generally excluded from the scheme.
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