The rate at which house prices are rising grew its fastest pace since June 2014, according to Halifax.
The mortgage lender said prices grew 9.7% in January compared with the same month in 2015, following growth of 9.5% in December. It said the last time prices grew faster was in June 2014, when growth was above 10%.
On a monthly basis, prices rose 1.7% between December and January. It means the average house price in the UK is now £212,430.
These figures are based on Halifax's own lending data, however. That often means there are considerable variation in the outlook for the housing market. For instance, Nationwide said prices had grown by just 4.4% in the year to January - less than half the growth identified by Halifax.
Martin Ellis, Halifax's housing economist, said: "The imbalance between supply and demand continues to exert significant upward pressure on house prices.
"This situation looks set to persist over the coming months. Further ahead, increasing affordability issues, as price increases continue to exceed wage growth, are likely to curb housing demand and cause price growth to ease."