House prices in May fell 0.2% from April in what Nationwide building society described as a subdued market.
The lender said “uncertainty” was likely to weigh on the market in the coming months.
Compared with a year earlier, house prices rose 0.6% – slower than the 0.9% rise the previous month.
Annual house price growth has been below 1% for six months in a row, according to data compiled by Nationwide.
“Survey data suggests that new buyer inquiries and consumer confidence have remained subdued in recent months,” said Robert Gardner, chief economist at Nationwide.
“Nevertheless, indicators of housing market activity, such as the number of property transactions and the number of mortgages approved for house purchase, have remained broadly stable.
“Housing market trends are likely to continue to mirror developments in the broader economy,” he said.
The number of first time buyers has continued to recover. According to Nationwide data there were 359,000 first-time buyers in the 12 months to March, just 10% below the 2006 peak.
“Even though house prices remain high relative to average incomes, the cost of servicing the typical mortgage as a share of take-home pay has remained close to or below long-run averages in most parts of the country,” Mr Gardner said.
The Nationwide said that almost half of first-time buyers had received help from friends and family to raise a deposit to buy a home.
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said that Brexit uncertainty was likely to have “instilled some caution in buyers”.
But he also expects a “modest” improvement later in the year, as consumer confidence has been recovering and mortgage deals have been getting better for buyers with smaller deposits.