The Halifax House Price Index showed that house prices in December were 6% higher than in the same month a year earlier.
But the month-on-month price increase of 0.2% was significantly down from the 1% increase seen in November.
Russell Galley, managing director at Halifax, said: "In the near-term, and with mortgage approvals still sitting at a 13-year high, there may be enough residual strength in the market to sustain prices up to the deadline for the stamp duty holiday and the scaling back of Help to Buy at the end of March.
"However, with the pace of the UK's economic recovery expected to be constrained by the renewed national lockdown, and unemployment widely predicted to rise in the coming months, downward pressure on house prices remains likely as we move through 2021."
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: "The availability of very cheap mortgage finance, albeit with some restrictions on high loan-to-value products, has helped fuel the surge in activity.
"The good news as far as this year is concerned is the re-emergence of 90% products, with HSBC a welcome return to the fray this week.
"COVID has given people the opportunity to focus on their housing requirements and what is important to them and their families."
Jeremy Leaf, a north London estate agent and a former Royal Institution of Chartered Surveyors (RICS) residential chairman, said: "Not surprisingly, the pace of house price rises started to slow in December, which is exactly what we found in our offices, as home movers were deterred by further lockdown restrictions and seasonal distractions.
"However, we recorded very few abortive sales, other than when chains had broken down or price renegotiations in response to reduced activity.
"Therefore, looking forward we expect the pattern to be repeated and the overwhelming majority of transactions to proceed to completion, followed by more balance between supply and demand as rollout of the vaccinations hopefully accelerates."