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.
Robert Gardner, chief economist at Nationwide, said: “Survey data suggests that new buyer inquiries and consumer confidence have remained subdued in recent months.
“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.