The Halifax has reported that house prices in the first three months of 2016 were 2.9% higher than in the final quarter of 2015.
The annual rate has grown from 9.7% to 10.1% in March.
The average price is now £214,811, the Halifax said.
Martin Ellis, Halifax housing economist, said: “Worsening sentiment regarding the prospects for the UK economy and uncertainty ahead of the European referendum in June could result in some softening in the housing market over the next couple of months.
“Current market conditions, however, remain very tight with an acute supply/demand imbalance continuing despite an improvement in the number of properties coming on to the market for sale in recent months. This, together with continuing low interest rates and a healthy labour market, indicate that house price growth is set to remain robust.”
“Another index, another rise in house prices – plus ca change,” said Jeremy Duncombe, director of Legal & General Mortgage Club.
“As wage growth and inflation fails to keep up to speed with the ever rising house prices due to undersupply, many first time buyers are feeling ever further away from the dream of property ownership.
“If we continue to ignore our housing crisis, we risk becoming a nation of renters not owners. In order to tackle this challenge, we need to explore all options to increase the amount of houses we build, right across the supply chain,” he added.