Nationwide said house prices declined by a monthly 0.4 percent following a fall of 0.3 percent in March which had been the first fall since mid-2015.
In annual terms, prices were 2.6 percent higher, the weakest increase in almost four years.
"While monthly figures can be volatile, the recent softening in price growth may be a further indication that households are starting to react to the emerging squeeze on real incomes or to affordability pressures in key parts of the country," Nationwide economist Robert Gardner said.
Economists polled by Reuters had expected house prices to rise by 0.1 percent in April from March and by 3.3 percent in annual terms.
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