Reassurances their money was safe has not been enough to prevent a repeat of the massive queues which began on Friday after Northern Rock announced it had agreed emergency funding with the Bank of England.

Customers are believed to have already withdrawn about £1 billion in savings from branches and through the internet since the news.

While queues in most towns were orderly, there have been angry scenes as upset customers voiced their frustrations over the bank's early Saturday closing, though many branches extended their hours.

In Sheffield, customers queuing outside the Pinstone Street branch urged the company to think again about closing at noon.

More than one hundred had joined the queue by 9.30am and the line stretched for about a hundred yards.

One woman said: "I'm at the back of the queue and I can't see myself getting in by 12. It's a disgrace. I just want to get all my money out and close my account."

Shortly before noon, a police sergeant addressed those still queuing with a megaphone and told them the office would close at 2pm and indicated a point in the queue after which people would not be served.

Northern Rock staff then took the details of those waiting beyond that point, with the guarantee they would be seen first on Monday, and the line dispersed.

In York, bank staff had worked until 9pm on Friday and began at 7.30am today to ensure they could process as many people as possible.

At 11.15am - 45 minutes before the branch was due to close - there were 160 people in the queue, which continued to grow despite warnings everybody might not be seen.

Senior staff spoke to customers and gave out letters which said the support of the Bank of England reflected a recognition Northern Rock was solvent.

In answer to the question: Are my savings safe? it said: "Yes. Our relationships with our customers are of paramount importance to us and there will be no change to your account or the service we will provide to you."

But customers were not convinced. One 77-year-old man said: "They are telling us our money is safe.

"But nobody is taking any notice. It is probably right what they have said. The money probably is safe but people have their money saved and are not prepared to risk it."

In Manchester, extra bank staff were drafted in and opening hours extended to cope with demand. The manageress at the Albert Square branch handed out drinks and sweets to elderly customers to reduce the tension, reassuring them staff would see all who were queueing.

In Cheltenham, a couple mounted a sit-in protest after being told that they couldn't withdraw £1 million from their account.

Former hoteliers Fiona and Christopher Howard refused to leave following a dispute with staff on Friday.

Police were called to resolve the situation and the couple eventually left empty handed.

Northern Rock has said its website is working, though slowly because of the volumne of internet traffic, if customers wish to make transactions over the weekend.