House prices increased by 1.4% compared with December 2018, Nationwide said, in line with the median forecast in a Reuters poll of economists.
In December alone, house prices rose by 0.1%, compared with a median forecast in the poll for no change.
Britain's housing market, along with the rest of the economy, has slowed since the 2016 referendum decision by voters to leave the European Union.
Last year's average price rise was weaker than gains of about 5% at the time of the referendum, according to Nationwide's index.
The lender said it expected house prices to remain broadly flat over the next 12 months.
"Looking ahead, economic developments will remain the key driver of housing market trends and house prices," Robert Gardner, Nationwide's chief economist, said.
"Much will continue to depend on how quickly uncertainty about the UK’s future trading relationships lifts as well as the outlook for global growth."
Prime Minister Boris Johnson led his Conservative Party to a sweeping victory in an election in December that paved the way for Britain to leave the EU at the end of this month.
Johnson has said he will strike a new trade deal with the bloc before Dec. 31, when a no-change transition period is due to end. EU officials have said that timetable might be too tight to reach a comprehensive deal.
Nationwide said house prices in London fell the most in 2019, down by 1.8%, though they are only around 5% below the all-time highs recorded in early 2017. The West Midlands was the best performing English region, with prices up by 2.7%, followed by the North, where prices were up 2.6%.
Prices in Scotland were up by 2.8% over the year.
(Writing by William Schomberg; editing by John Stonestreet)
