Average house prices between March and May were up 9.2% on the same period in 2015, and increased by 1.4% compared with the quarter from December to February.
On a monthly basis, house prices increased by 0.6% between April and May 2016.
Martin Ellis, Halifax housing economist, said demand versus supply had contributed to a rise in prices, but that this should ease.
“Low interest rates, increasing employment and rising real earnings, continue to support housing demand,” said Ellis.
“The strength of demand, combined with very low supply, is causing house prices to rise at a brisk pace in quarterly and annual terms.
“Increasing affordability issues, caused by a sustained period of higher-than-earnings house price growth, should curb housing demand and result in some slowdown in house price growth as the year progresses.”
Halifax found that the average price of a house in the UK in the three months to the end of May was £213,472.
North London estate agent and former chairman of the Royal Institute of Chartered Surveyors, Jeremy Leaf, said a shortage of housing stock continued to be an issue.
“It is encouraging for the longer-term health of the market that property prices haven’t dropped substantially following the introduction of the Stamp Duty surcharge for landlords and second homeowners at the beginning of April,” said Leaf. “But it is clear that house prices are being underpinned by a shortage of stock and substantial reduction in transaction volumes.”
He said that once EU Referendum has past, the true state of the market will be seen.
“Once the vote is out of the way and the result is in, hopefully the market will settle down again very soon after,” he said.