The typical home in the UK cost £220,100 in April, a rise of £3,500 on the previous month, official figures show.
This was a £12,000 increase from the same month a year ago, the Office for National Statistics (ONS) said, despite lenders reporting a relatively stagnant housing market.
House prices rose sharply in Scotland over the year, the ONS said.
Meanwhile, the cost of renting a home rose by 1.8% in a year, the ONS said.
The ONS said that average house prices in the UK have increased by 5.6% in the year to April, accelerating from 4.5% in the year to March.
This contrasts with recent figures from the Nationwide Building Society and Halifax Bank, which have shown the market stalling in recent months.
"These figures go against the recent trend of a Brexit-related slowdown that we predicted last year but remain consistent with our guidance of 2% to 5% growth in 2017 as a whole," said Richard Snook, senior economist at accountants PwC.
The ONS survey includes cash buyers but economists point out that it still uses only a small sample of transaction data - making the short-term conclusions prone to fluctuations.
Over the course of the year to April, the fastest house price rises among the nations of the UK was 6.8% growth in Scotland.
Among the English regions, prices went up fastest in the East of England, rising by 8.1%. The slowest was a 0.6% rise in the North East.
The annual growth in the cost of renting has slowed from 2.5% a year ago to 1.8% now. Research published on Monday showed that affordability of rent and house buying was the biggest issue for tenants of private landlords.
In separate figures, the ONS said that prices in general, as measured by inflation, rose by 2.9% in the year to May - driven by the cost of foreign package holidays for British tourists, and the price of computer games and equipment.