Monthly figures from the Land Registry put the annual rate of house prices increases in England and Wales at 4.6 per cent in May, down from 5.1 per cent.
The price of the average home was virtually unchanged between April and May at just under £180,000.
Earlier, the latest UK-wide house price index from the Office for National Statistics suggested the rate of increase was falling back even faster.
The ONS figures, covering the 12 months to April, showed that the annual rise had fallen to 5.5 per cent from 9.6 per cent.
It added that the average price had actually fallen over April itself, as the London market stalled.
A rapid gain in values earlier last year ran out of steam after the imposition of much tighter rules on how much buyers could borrow.
Meanwhile, the Council of Mortgage Lenders reported that lending to first time buyers had declined.