The bank, which has 100,000 borrowers, is dropping its rate to 7.49 per cent. This takes effect immediately for new borrowers and from 5 January for existing borrowers.
A building society also cut its mortgage rates yesterday - but only for new borrowers. New customers at National and Provincial Building Society will receive an immediate cut of 0.25 per cent, bringing the standard rate down to 7.74 per cent.
But 375,000 existing borrowers will not see a change in their rates until after the Budget. Chris Herbert, manager of mortgage products at the eighth-largest society, said: 'We think the base rate coming down is very positive, and we wanted to pass it on to new borrowers, especially first-time buyers. There may be a further cut on Budget day itself, or perhaps in December. I don't think they will wait until January.'
The Royal Bank of Scotland said it was keen to expand its mortgage business. Frank Kirwan, director of retail banking services, said: 'We are happy to be the first to pass on to house-buyers the full benefit of this week's 0.5 per cent fall in base rates.'
The two other lenders that have announced a cut in rates, Nationwide Building Society and NatWest Bank, have cut their rates by 0.25 per cent.
Others are waiting to see how the Budget affects the housing and savings market before making a move. John Fry, group services director at Abbey National, said: 'One week before the Budget is not the right time to take a decision.'
John Wriglesworth, housing analyst at the stockbrokers UBS, said lenders might trim mortgage rates by just 0.2 per cent, or 0.3 or 0.4 per cent, if there is a further 0.5 per cent fall in base rates.
More than half of new borrowers take out fixed-rate loans. These will not be affected by this week's base-rate cut. The money markets have been anticipating at least a 0.5 per cent drop in rates, with some traders looking to a full
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