On a monthly basis and seasonally adjusted, prices fell by 0.7 per cent, in sharp contrast to the 0.4 per cent figure recorded for November.
The figures will fuel fears that the housing market is running out of steam and could face a correction or even a crash in the coming months.
House prices also fell by 1.4 per cent in the Outer Metropolitan area, which includes Reading, Slough, Windsor and Maidenhead and Wokingham. The rest of the South East stagnated.
Northern Ireland was the strongest performer, with house prices in the fourth quarter of 2018 up by 5.8 per cent annually to reach £139,599 on average, followed by the East Midlands and Wales, where house prices lifted by 4 per cent annually.
The Bank of England governor, Mark Carney, said last month that in the event of a "disorderly" departure from the European Union - not the central bank's base-case scenario - house prices could slump by 30% as part of a broader economic shock. In the capital, the average price in the fourth quarter of 2018 was £466,988 - 0.8 per cent lower than the same period in 2017.
The uncertainty of Brexit is also denting demand and clouding the economic outlook.
House prices in London, and in some commuter zones, have declined year-on-year.
Nationwide said it expected prices to rise at a "low single-digit pace" in 2019 but its forecast was dependent on the economy continuing to grow modestly, something that looked "unusually uncertain". "This more nuanced picture obviously isn't reflected in the headline figures, but as the current political and economic uncertainty continues, could well continue to be the case until such times as more clarity is available".
Mr Gardner said the North-South house price divide in England narrowed in 2018.
"The Nationwide numbers are one of the most comprehensive and well-established reports of housing market activity so command respect", said Jeremy Leaf, north London estate agent and a former Royal Institute of Chartered Surveyors residential chairman.
EY ITEM Clubs's chief economic advisor Howard Archer warned house prices could tumble in an event of a no deal.
He said: "Looking forward, this is always a fairly quiet time anyway for the market so the reasonable start we have had to business won't be seen in the figures for at least the next month or so".
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: "Lenders remain keen to lend and mortgage deals competitive".