The housing market continued to slow in February with prices falling a seasonally adjusted 0.5%, the Halifax has said.
The drop meant the annual rate of house price inflation was at 12.1%, down from 13.7% in January.
This is the lowest annual rate since an 11.7% growth figure recorded in December 2001, Halifax added.
The figures are in contrast to the latest data from the Nationwide which showed prices rose 0.5% in February.
"This continues the mixed pattern of monthly price rises and falls recorded since last summer and is consistent with a gradual slowdown in house price inflation," Halifax chief economist Martin Ellis said.
Annual house price inflation has slowed dramatically from a peak of 22.1% in July. Since July prices have risen just 0.8%.
The average price of a property is now £162,816 the bank added.
The amount of houses being sold has risen, says Halifax
However, signs of increased sales activity emerged from the survey.
In each of the past two months Halifax Estate Agents have seen an increase in the number of sales agreed.
Likewise, on Tuesday, the Nationwide said slowdown in buying activity had bottomed out and that annual house price inflation stood at 10.2%.
Halifax warned that a strengthening in the housing market over the next few months could trigger another rise in the cost of borrowing from the Bank of England, taking base rates to 5.0%.
The jobs market is also continuing to strengthen, with the number of people in employment rising by nearly 300,000 over the past year.
"This ongoing development continues to provide a solid support for the housing market, helping to maintain its sound underlying health," said Martin Ellis.
On the other hand, "continuing evidence of a slowdown in both the housing market and consumer spending growth" would, it said, be enough to avert another rate rise in the near term.
Meanwhile, the percentage of earnings the average first-time buyer is spending on their mortgage has risen from a 20 year low of 13% in September 2003 to 20% now.
This proportion is just above the 19% average for the past 20 years and compares with the 34% peak seen in 1990.
Flying Kite marks
Efforts to protect house buyers from unscrupulous mortgage lending tactics are continuing.
Last year, measures were put in place to make sure all mortgage sellers were licensed.
Now estate agents are being encouraged to apply for a British Standards Institution 'Kite' mark. Under the scheme if agents want to join up, they will ask BSI Inspectors to visit them and check their business practices and customer records.
Supporters of the Kite mark plan say that reliable estate agents will sign up for the voluntary scheme, while rogue operators will not.
Importantly for estate agents, the BSI's experience in other industry sectors has shown that companies which gain the Kite mark see a marked increase in business.
But dissenters believe the Kite mark scheme will offer little more than another measure, the National Ombudsman Scheme. The mandatory scheme will come into effect in 2007.