Housing supply is down by 27% since May last year, down to just 44 properties per branch.
The drop has caused buyers to increase their asking price in order to drive off competition.
Some 19% of properties sold for more than the asking price in May, nearly three times higher than recorded in September 2013.
And only 46% of sellers accepted lower than the asking price, representing the lowest monthly percentage ever.
NAEA agents also reported an increase in the average number of house sales, up from nine to ten properties in May.
Rising house prices have also resulted in a decline in the first-time buyer market, with the proportion of FTBs purchasing in May shrinking to 25%, down from 28% in April.
Mark Hayward, managing director at NAEA, said: “The number of house-hunters is substantially higher than the number of properties on the market, so competition is always going to be rife.
“Unfortunately the housing problem is not going to go away anytime soon. With limited numbers of houses for sale, those who simply can’t afford to increase their original offer will often be priced out the market.
“With current speculation on interest rates rising, we could see more homeowners putting their houses on the market in a panic that house prices may reduce as a result of interest rate and mortgage rate hikes,” he said.
“However the new Mortgage Market Review rules may also create mortgage prisoners who cannot gain new mortgages for house moves, which combined with rising house prices, could result in a slowdown of house sales which could take the heat out of the property market.”