RICS' house price balance, which measures the difference between the percentage of surveyors seeing rises and falls in house prices, increased to -30 last month from -39 in April.
However, analysts are forecasting another slowdown for the housing market with markets largely expecting the BoE's Bank Rate to peak at 5.5% later this year, up from 4.5% now.
Britain's housing market staged a recovery earlier this year after former prime minister Liz Truss's "mini-budget" caused turmoil in financial markets in September and sent the cost of fixed mortgage rates sharply higher to above 6%.
Britain's biggest mortgage lender, Halifax, on Wednesday said house prices dropped by 1.0% year-on-year in May, the first annual decline since 2012.
Some mortgage lenders, including Halifax and Nationwide Building Society have ramped up their fixed mortgage rates in response to the rise in borrowing costs in financial markets.
Persons:
RICS, Tarrant Parsons, Liz Truss's, BoE, Suban Abdulla, William Schomberg
Organizations:
Bank of England, Royal Institution, Chartered Surveyors, Nationwide, Nationwide Building Society, Thomson
Locations:
April's, Halifax