Areas such as London and the South East could see the inflated cost of getting onto the housing ladder increase even more, it was warned.
Home sales in the UK reached a four-year high last month, according to the figures, as surveyors on average saw 18.7 transactions each in the three months to September.
While the level remains historically low, it is the strongest since November 2009, amid a housing market that is picking up across the country, the figures from the Royal Institution of Chartered Surveyors (Rics) show.
The market has been boosted by the Government's Help to Buy initiative. A second phase of the scheme introducing mortgage guarantees being launched is expected to add to demand.
The Rics survey showed that prices had continued to grow, with a balance of 54% more surveyors reporting rises rather than falls.
It found that they had now been rising steadily since Easter. Last month, they increased in every region of the UK except the North East - where they dropped modestly for the second successive month.
Respondents were upbeat about the number of transactions increasing over the next three months as well as price rises.
Peter Bolton King, Rics global residential director, said: "It's encouraging that the market is starting to improve in all parts of the country with more buyers looking to make a move and more sales going through.
"Even so, it's a big concern that the supply of property coming to the market is lagging so far behind demand.
"This imbalance is likely to result in further upward pressure in prices over the coming months, particularly in the nation's hotspots."
The report said Help to Buy had a key role in driving the housing market recovery, together with the Bank of England's Funding for Lending scheme to ease borrowing conditions.
It added: "London and the South East remain the areas under the greatest price pressures with the overwhelming number of respondents in each region pointing to price rises."