The Outer Metropolitan area fell by 1.4 per cent to see house prices fall to £356,531.
Compared with a year earlier, prices rose by just 0.5 percent compared with a 1.9 percent rise in November.
Mortgage Advice Bureau head of lending Brian Murphy comments: "The softer year on year average growth figure of 0.5 per cent is within market expectations for 2018, however one might suggest that this masks the better performance of some regions... and consumer confidence has remained resilient for much of the year".
House prices were down by 0.7% month-on-month in December.
"I think that in the longer term, there are reasons to believe that on-average housing prices in the United Kingdom, which have risen enormously in the last 20 to 30 years, will rise over the medium-term", Dr.
House prices in London, and in some commuter zones, have declined year-on-year.
In London, the average house price in the fourth quarter of 2018 was £466,988 - 0.8% lower than the same period in 2017.
The regional picture is varied, with prices in Northern Ireland performing the best in the United Kingdom with a growth rate of 5.8% in 2018.
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Annual house price growth slowed to 0.5 per cent, Nationwide said on Friday, compared with a rise of 1.9 per cent in November and weaker than a median forecast of 1.5 per cent in a Reuters poll of economists.
Robert Gardner, Nationwide's chief economist, said that an "unusually uncertain" economic outlook is taking its toll on prices.
"We would expect United Kingdom house prices to rise at a low single-digit pace in 2019", he said. Scotland and England reported much slower growth at 0.9 and 0.7, respectively.
Mr Gardner said the North-South house price divide in England narrowed in 2018.
This trend was not entirely unexpected, however, as it followed several years of sustained outperformance by the south which left affordability more stretched in these areas.
Since the vote, the housing market has weakened, led by price falls in London.
"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".
EY ITEM Clubs's chief economic advisor Howard Archer warned house prices could tumble in an event of a no deal.
But Mark Harris, chief executive of mortgage broker SPF Private Clients, offered some optimism on the outlook: 'Lenders remain keen to lend and mortgage deals competitive.