Construction of new homes spurted by 10.8 percent last month, reversing September's sharp and unexpected decline, the government reported yesterday.

Meanwhile, the Veterans Administration provided another boost for the housing industry by cutting the maximum interest rate on loans it backs from 11.5 to 11 percent, the lowest level in more than six years and the fourth VA rate cut this year.

The twin dose of upbeat news left housing and lending industry officials in an exultant mood after the puzzling 9.3 percent drop in housing starts in September. That drop occurred despite the continued decline in mortgage rates, which now hover in the 11.5 to 12 percent range for 30-year, fixed-rate loans, with some adjustable-rate mortgages starting another two percentage points or more lower.

Warren Lasko, executive vice president of the Mortgage Bankers Association of America, described the September decline in housing construction as "an aberration. I guess that was a month where builders looked at their inventory and pulled in their horns," he said. "The October rates are much more in line with demand" for new housing.

The Commerce Department report pegged October housing starts at an annual rate of 1.760 million, up 10.8 percent from the revised September figure of 1.589 million. The October figure would seem to indicate that the final 1985 total will reach 1.7 million or more for the third straight year, a healthy rate for an industry that often has had to cope with wide fluctuations in production from year to year.

"Those are very encouraging figures," Lasko said. "To some extent, with adjustable-rate mortgages, we've taken out the peaks and troughs of housing starts" by creating financing arrangements so that "people will be able to afford a house and not wait until the next time mortgage rates come down. It makes housing the one ray of hope in the economy," he said, with consumer buying and investment spending more sluggish at the moment.

John J. Koelemij, president of the National Association of Home Builders, attributed "the strong performance by housing in October to the lowest mortgage rates since 1979 and a strong demand for single-family housing in many areas." But he noted that the overall favorable national housing construction figures are predicated on boom times in some sectors that outweigh declines elsewhere.

"The Northeast is having a banner year, with building permits up 38 percent from a year ago," Koelemij said. "The Midwest, as well as California, Virginia, Maryland, North Carolina and Florida, are doing well. The big losers are the states of Texas, Oklahoma, Colorado, Louisiana, Arizona and New Mexico," where construction has dropped during the first nine months of the year compared with the same period in 1984.

James Christian, chief economist for the U.S. League of Savings Institutions, said the October construction report "indicates housing is back on track. September is probably the hard one to explain, when housing starts slumped sickeningly. I like the composition of the increase , up in the single-family area. That's where the building ought to be."

The Commerce figures showed that single-family house construction accounted for most of the October increase, with new building at an annual rate of 1.123 million units, up 15.8 percent over September.

In the only negative aspect of the monthly report, the government said that the number of building permits issued in October actually declined over September, down 7.2 percent to an annual rate of 1.675 million, which could be a harbinger of a construction slack.