All UK financial institutions are clear of the red danger zone with their Year 2000 work, according to the Financial Services Authority (FSA).
The UK's chief financial regulatory body said in July that two financial institutions, which it refused to name, had a red classification - a warning of serious risk of material disruption to the business.
A spokesperson for the FSA said: "The two that were red are now in the amber zone." Amber represents an organisation behind with its bug preparations, but not facing serious disruption come the rollover.
The spokesperson said that the number of organisations on track in the blue zone has leapt from 72 per cent to 95 per cent since that time.
Meanwhile the amber zone contains only five per cent - a drop from 28 per cent in July.
The spokesperson said: "Out of 415 firms, a little over 20 are in the amber zone. We have seen great progress over the summer, but this is no excuse for complacency. They must keep vigilant or there is the worry that they could slip back."
He added: "We believe it will be business as usual in the New Year and that people should not worry. However, it does not mean that every single thing will work."
Ian Hugo, assistant director of millennium bug pressure group, Taskforce 2000 said: "I'm not worried about the financial institutions individually. It's the interconnections between them such as ATMs. The banks have a lot of cross dependencies, but they should have tested most of them."
Hugo said the factor for most concern is public confidence: "Some of the other European countries haven't done as well in the financial sector. If an Italian bank goes pear-shaped, it could have a knock-on effect on public confidence."
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