The number of homes sold in the UK in June rose by 21% from May to 86,000, HM Revenue & Customs has said.
The sales figures were the highest this year and were up 15% on the same month last year.
It means sales in the first half of 2010 have been 21% higher than in the first six months of 2009.
The Royal Institution of Chartered Surveyors (RICS) said the figures meant house sales were still subdued.
"Sales are still running well below the levels preceding the onset of the credit crunch, partly because of a shortage of mortgage finance as well as, until recently, the lack of stock on the market," a spokesman said.
Lenders have become sceptical that their mortgage lending will rise much further this year.
On Tuesday, the Bank of England warned that the tight supply of mortgages might become worse in the coming months, which could stop sales growing faster.
The renewed rise in house prices, which started in the spring of 2009, now seems to have reached a plateau, according to the most recent surveys from the Nationwide Building Society and the Halifax Bank.
RICS recently forecast that prices may fall in the latter part of the year if the increasing number of homes for sale outnumbers potential buyers.