The closely watched house price index from Nationwide, one of the UK's biggest mortgage lenders, showed a 0.2% month-on-month rise for June.
That was narrower than the 0.4% seen in May. But June's annual rate of growth rose to 1.5%, up from 1.3%.
London outpaced the national rate, with prices in the capital up 1.6% to an average of £525,248. The national average house price was £266,604.
Daniel Austin, CEO and co-founder at lender ASK Partners, said: "The property sector is recovering.
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