The mortgage lender said that while house prices continued to climb in May, with prices up 10.5% in 12 months, this was slowest rate of growth since the start of the year.
The rise meant the average price of a house hit another record of £289,099.
Halifax said that house prices have now climbed for eleven consecutive months.
“Despite the very real cost of living pressures some people are experiencing, the imbalance between supply and demand for properties remains the primary reason driving the continued climb in house prices,” said Russell Galley, managing director at Halifax.
“However, the housing market has begun to show signs of cooling. Mortgage activity has started to come down and, coupled with the inflationary pressures currently exerted on household budgets, it’s likely activity will start to slow,” he added.
“So, there is perhaps one green shoot for prospective purchasers; with overall buying demand down compared to last year, we may be past the peak sellers’ market.”
Estate agents said the survey from Halifax confirms what they are seeing on the ground.
“The cost of living crisis and successive interest rate rises are finally having an impact on the housing market,” said Jeremy Leaf, a North London estate agency owner and a former Royal Institution of Chartered Surveyors (RICS) residential chairman.
“Prices are still rising but not as rapidly as they were just a few months ago and activity is cooling.”
However, Mr Leaf said a major correction seemed “unlikely” while housing stock remained low, particularly for in-demand properties such as three- and four-bedroom family homes.
According to Halifax, house prices increased by 1% month-on-month in May. It added that they had shot up by some 74% over the last 10 years.
The strongest inflation in that period has been in London (84.2%), followed by the East of England (84%) and the East Midlands (82.1%).
Danni Hewson, a financial analyst at AJ Bell, said the latest figures were “cold comfort” to people trying to get onto the property ladder.
“Cooling, definitely but the housing market is unlikely to come off the boil, at least for the foreseeable future especially as it’s becoming harder and more expensive to find places to rent.”
She added that the “age old problem” of demand outstripping supply wouldn’t go away without a period of “unprecedented housebuilding”.
“And with money so tight at the moment, anyone who might have been thinking of hoisting the for-sale sign will probably hold off until inflation returns to something resembling normal,” she added.
Inflation – the rate at which prices rise – hit 9% in April, a 40 year high.
The Bank of England has warned inflation might reach 10% within months, as the prices of fuel and food put pressure on household budgets.