Nationwide's house price index showed prices rose 4.5 per cent in the year to December, up from 4.4 per cent in November, its lowest rate since January.
On a monthly basis, prices rose 0.8 per cent, up from no growth in November. That put the average UK house price at £205,898, up from £204,947 last month.
The astronomical growth in London's house prices has slowed in recent months, and Robert Gardiner, Nationwide's chief economist, suggested the slowdown may continue.
"There were signs that London's significant period of outperformance may be drawing to a close," he said.
"For the first year since 2008, annual house price growth in the capital was lower than the UK average, with prices increasing by 3.7 per cent over the year, down from 12.2 per cent in 2015."
Earlier this month, figures from the Royal Institution of Chartered Surveyors suggested the capital's house price growth will stagnate next year after changes to the tax regime aimed at decreasing the number of second home buyers, while demand from tenants is stagnating.
Meanwhile, research from Propcision showed some luxury London properties have had their prices cut by as much as a third, while prices in top-end areas such as Chelsea have dropped by 13 per cent this year.
"We believe the fundamentals for house buyers will progressively deteriorate during 2017 with consumers’ purchasing power weakening markedly and the labour market likely softening," said Howard Archer, chief UK and European economist at IHS Global Insight.
"Increasing economic uncertainty is also likely to weigh down on consumer confidence and willingness to engage in major transactions such as buying a house. Housing market activity and prices are also likely to be pressurised by stretched house prices to earnings ratios and tight checking of prospective mortgage borrowers by lenders."