According to Reuters, House prices increased 0.6 percent in May compared with a year ago after rising by 0.9 percent in April.
A Reuters poll of economists had pointed to a-1.2 percent rise in May.
House prices in May fell 0.2 percent from April, when they grew 0.3 percent on the month Nationwide said.
The figures looked at odds with other tentative signs that activity in housing market is gradually picking after slowing sharply through 2018.
While house prices have been rising across the country as a whole, prices in London have fallen according to various indicators, hit by unaffordable prices for many buyers, tax changes and Brexit uncertainty.
“Nationwide’s data confirm that house prices remain on an essentially flat trend, primarily because Brexit uncertainty has instilled some caution among buyers,” economist Samuel Tombs from Pantheon Macroeconomics said.
“The trend likely won’t improve in the next couple of months, given the political deadlock in Westminster.”