Prices between April and June rose 3.7% on a year earlier to an average of £167,984, the biggest increase since August 2010, mortgage lender Halifax said. Values in June were 0.6% higher than May, the fifth consecutive month of rises.
Lenders, builders and estate agents have been reporting better conditions in recent months, as state schemes including Help to Buy and Funding for Lending (FLS) spur a market recovery.
Mortgage approvals soared to their highest level in three-and-a-half years in May, with 58,242 loans approved for house purchases, the Bank of England said recently. That was up from 54,354 in April and the highest level since December 2009.
The FLS incentivises banks and building societies to lend more in return for discounted loans, and has been credited with improving mortgage availability and reducing rates.
Chancellor George Osborne also unveiled Help to Buy in March, which allows people to buy a property with a 5% deposit. The state lends buyers 20% of the value of a new home worth up to £600,000, interest-free for five years.
Bank of England deputy governor Paul Tucker this week said anything more than a short-term Government guarantee of mortgages would be unwise and could sow the seeds for another housing crisis.
Halifax housing economist Martin Ellis said: "Improved confidence in both the housing market and the economy, combined with a shortage of properties available for sale, appear to be pushing up house prices. The Funding for Lending Scheme is also likely to be boosting the market by helping to reduce mortgage rates. There are also early indications that the Help to Buy equity loan scheme may be stimulating demand."
But the lender added that housing supply remains tight, citing figures from the Royal Institution of Chartered Surveyors showing the stock of unsold properties was down 5% in May year-on-year.