LONDON—A member of the Bank of England's rate-setting Monetary Policy Committee Tuesday said he is "concerned" about the U.K. housing market after official figures showed house prices accelerated in August to hit their highest level on record.

Prices across the U.K. rose 0.5% in August from July and were up 3.8% from a year earlier, the fastest annual increase since October 2010. That left the index of prices at its highest level since records began in 1968, the Office for National Statistics said.

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