The number of new houses started in June plunged 15.3 percent from May, the Commerce Department reported yesterday, prompting housing economists to predict that 1982 will be the worst year for housing since World War II.

After hitting a post-war low of 1.1 million units last year, the housing industry had hoped a recovery would begin this year, but those hopes appear to have ended with yesterday's report.

June starts were at a seasonally adjusted annual rate of 911,000, 13 percent below last year's depressed level.

"I just lost a bet with our president, because I said starts would be over 1 million this year," said Mark Riedy, executive vice president of the Mortgage Bankers Association. April, May and June normally are the highest months for new home starts, so "it is hard to see any bright spot on the horizon," he said.

Bolstered by multifamily housing construction, starts in May had risen to an annual rate of 1.075 million, exceeding the 1 million a year pace for the first time this year. President Reagan used the figure as a sign that the economy was starting to turn around, but members of the housing industry said the rise was merely an aberration caused by a spurt of federally subsidized rental apartments. Construction on these projects was made possible by belated budget increases, mainly in programs the administration plans to end after this fiscal year.

"The May figures were like a groundhog that came out and saw its shadow and ran back," Riedy said. "This means a long, hard winter for housing still ahead."

"We have to say 'I told you so,' " said Fred Napolitano, president of the National Association of Home Builders, pointing to the administration's claim that an upturn had begun in May. "Every month that goes by we are going to see more and more builders, contractors and suppliers going out of business."

Jack Carlson, chief economist for the National Association of Realtors, pointed out that the level of building permits as announced yesterday by the Commerce Department remained essentially flat between May and June, at an annual rate of 948,000. This is an indication that there will be no pickup in starts three months from now, he said. Permits for single-family homes rose 5 percent from May, while those for multifamily housing fell 5 percent.

Carlson predicted that mortgage interest rates might go down a percentage point from their current level of 16 1/2 to 17 percent by the end of the year but then could go back up above 17 percent because of heavy government borrowing at the end of the year.

The largest drop in starts in June was in the multihousing area, which fell 39 percent from May to a rate of 216,000 units.

For the first six months of this year, housing starts were 25 percent below their 1981 level, 451,200 units this year compared with 602,900 last year.