The latest House Price Index from Nationwide also shows that home ownership rose for third year running.
Property prices fell by 0.3% between December and January, according to Nationwide's House Price Index.
On an annual basis, house price growth slowed to 6.4%, from 7.3% in December.
In addition, the data shows that home ownership rose for third year running.
Robert Gardner, chief economist at Nationwide, said: “To a large extent, the slowdown probably reflects a tapering of demand ahead of the end of the stamp duty holiday, which prompted many people considering a house move to bring forward their purchase.
“While the stamp duty holiday is not due to expire until the end of March, activity would be expected to weaken well before that, given that the purchase process typically takes several months (note that our house price index is based on data at the mortgage approval stage).
“The typical relationship between the housing market and broader economic trends has broken down over the past nine months.
“This is because many peoples’ housing needs have changed as a direct result of the pandemic, with many opting to move to less densely populated locations or property types, despite the sharp economic slowdown and the uncertain outlook.
“Indeed, the total number of mortgages approved for house purchases in 2020 actually exceeded the number approved in 2019, and house price growth ended 2020 at a six-year high, even though the economy was probably around 10% smaller than at the start of 2020, with the unemployment rate around a percentage point higher.
“Looking ahead, shifts in housing preferences are likely to continue to provide some support for the market.
“However, if the stamp duty holiday ends as scheduled, and labour market conditions continue to weaken as most analysts expect, housing market activity is likely to slow, perhaps sharply, in the coming months.”
Nicky Stevenson, managing director at Fine & Country, added: “A predicted collapse in house price growth has failed to materialise.
“This was supposed to be the month that legions of buyers effectively threw in the towel and moderated their offers having been forced to remove the stamp duty tax break from the equation.
“Yet, despite everything, this market is still clinging firmly to strong annual price increases and this is further evidence that, while the stamp duty tax break was a catalyst for the mini-boom, it’s not the main motivator pouring fuel on this fire.
“This isn’t really that surprising.
"By the end of last year, the market’s gains had already eroded the tax benefit of the Chancellor’s scheme, which already suggested there was more going on.
“Those who benefit least are also those more likely to be older, with families and most in need of more space.
“These households are also more likely to have the money to make that move happen. They are responsible for the narrative that has characterised the past nine months.
“Continued talk of negative interest rates isn’t doing anything to cool demand for mortgages either and the housing market could still have a few more surprises up its sleeve this year.”
Miles Robinson, head of mortgages at Trussle, added: "The slight month-on-month decrease in house prices represents the first signs of a slowdown since the property market was initially suspended in March 2020.
"As we approach the end of the stamp duty holiday on 31st March, we could start to see chains falling apart as some buyers may be unable to move ahead without the extra finance the stamp duty holiday would give them. The housing market is starting to reset.
"As well as impacting current growth, the cliff edge stamp duty holiday deadline also poses a risk to property transactions still underway.
"It’s estimated that as many as 105,000 property transactions currently underway could miss the stamp duty deadline.
"This is partly because the holiday triggered unprecedented demand in the market which created delays in processing house purchases, and means it currently takes 134 days to complete a property in the UK.
"Local searches in particular are facing delays, with some areas now experiencing waiting times up to 200 times longer than normal.
"There has been much speculation about whether the stamp duty deadline should be extended to avert a shock to the market.
"MPs have also recently suggested whether a gradual tapering of the scheme would be a more effective and fair way of bringing it to a close, which is certainly worth considering if we see growth continue to slow moving forwards."
Mike Scott, chief analyst at estate agency Yopa, said: "Nationwide has reported a slowdown in house prices in January, as the March stamp duty deadline draws near.
"Average house prices were down by 0.3% for the month, and the annual rate of growth has fallen from 7.3% to 6.4%.
"A slowdown in this measure of housing market activity was expected for the first quarter of 2021, because the boost from the stamp duty holiday has largely passed.
"Nationwide’s figures are based on mortgage approvals, and if your mortgage was approved in January you were probably already too late to complete the purchase before the end of March and thus avoid paying stamp duty.
"We expect that the figures will weaken further in the coming months before recovering in the second half of the year, as the pandemic recedes and many people look for a fresh start in their lives, which may well involve a house move."
