House prices increased by 0.6% month-on-month in August to reach a new record of more than £206,000, an index has found.
The average UK property value is now £206,145 after climbing by 5.6% annually, Nationwide Building Society said.
Despite recent reports that housing market activity has slowed, the rates of price growth accelerated in August, Nationwide said.
In July, prices increased at lower rates of 0.5% month-on-month and 5.2% annually.
Nationwide said that while buyer demand has softened, the number of new homes coming to market has also been low. This has kept the balance of demand and supply tight, which in turn has supported prices.
A Bank of England report showed this week that the number of mortgage approvals made to home buyers fell to its lowest level in a year and a half in July, in signs that the vote to leave the EU had a cooling effect on the market.
A stamp duty hike for buy-to-let investors, which came into force on April 1, has also put the brakes on some activity.
Robert Gardner, Nationwide's chief economist, said: "The pick-up in price growth is somewhat at odds with signs that housing market activity has slowed in recent months.
"However, the decline in demand appears to have been matched by weakness on the supply side of the market. Surveyors report that instructions to sell have also declined and the stock of properties on the market remains close to 30-year lows. This helps to explain why the pace of house price growth has remained broadly stable."
Average house prices broke through the £200,000 barrier in March and have been steadily climbing since.
Mr Gardner said what happens next on the buyer side of the housing market will largely hinge on the the outlook for the labour market and confidence among house hunters.
He said: "It is encouraging that the unemployment rate remained at a 10-year low in the three months to June, though labour market trends tend to lag developments in the wider economy. It is also positive that retail sales increased at a healthy rate in July."
But he continued: "Business surveys suggest that the manufacturing, services and construction sectors all slowed sharply in July, and, if sustained, this is likely to have a negative impact on the labour market and household confidence.
"Most forecasters, including the Bank of England, expect the economy to show little growth over the remainder of the year."
Mr Gardner said the Bank of England's decision to lower the base rate to 0.25% will provide an immediate benefit to many mortgage borrowers who will see their repayments become cheaper, although "for most the boost will be fairly modest", with the typical saving from the base rate cut being around £15 per month.
Jeremy Leaf, a north London estate agent and former residential chairman of the Royal Institution of Chartered Surveyors (Rics), said: "While the increase in prices in August is encouraging and a little surprising, when you look behind the figures it becomes apparent that most of it is based on shortage of stock which we are also finding on the ground."
He continued: "We are finding that an appetite to get on with buying and selling from those returning from holiday has been encouraging lately and we hope that continues into the autumn. People are negotiating very hard to make the deals that are being done happen."
Howard Archer, chief UK and European economist at IHS Global Insight, said: "Despite the resilient house price growth in August reported by the Nationwide, we expect house prices to come under increasing pressure over the coming months."