A new drive for handgun controls, inspired by the small suburb of Morton Grove, Ill., is spreading across the country with a vigor that surprises both sides of the issue.

A ban on handguns, patterned after the Morton Grove law, was proposed by San Francisco Mayor Dianne Feinstein last week, as a Chicago City Council committee was approving Mayor Jane Byrne's new proposal for a freeze on handgun ownership.

East St. Louis, Ill., recently enacted a ban on possession outside the home. New handgun control measures of varying strictness have been proposed, or are about to be proposed, in Houston, in Dade and Broward counties, Fla.; in Santa Monica and Alhambra, Calif., and in the legislatures of Massachusetts and Maryland.

More can be expected. James Sloan, Morton Grove village administrator, said that about 400 jurisdictions have requested copies of the Morton Grove ordinance.

Most of the action has come since Dec. 29, when a U.S. District Court upheld the Morton Grove ordinance, rejecting the traditional argument that the Constitution prohibits a ban on handguns.

A month later a state court in Illinois rejected a challenge under state law. An appeal is in progress, and the issue is expected to reach the U.S. Supreme Court by late 1983.

Officials of the National Rifle Association, the leading gun control opponent, say they have never seen anything like it. There are more proposals "by far" than ever before, said Michael Lashbrook, director of state and local affairs for the NRA. The NRA and its affiliated gun clubs continue to battle each of them, he said.

Paul Lavrakas, field director for the National Coalition to Ban Handguns, calls it a "chain reaction."

"It really started with the death of John Lennon and the shootings of President Reagan and the pope. Then the movement was supposed to die away like it has in the past," he said. "It didn't. The main reason for that was Morton Grove."

Morton Grove, a suburb of 25,000 northwest of Chicago, enacted the toughest handgun law in the country last June after a bitter fight with local gun clubs. The ordinance, prompted by a neighborhood organization's complaints about plans for a gun shop, banned sale and possession of handguns in the village with exemptions for police, military and gun clubs. Residents were supposed to turn in their weapons to local authorities.

Since the law went into effect a few weeks ago 11 people have turned in guns, according to Sloan. He said he does not know what percentage of Morton Grove's handguns that represents, but concedes that it is a small fraction.

Sloan said village trustees anticipated that few handguns would be turned in, but he said they hoped to start a nationwide trend that would, in the long run, puncture "the myth promulgated by the NRA" that bans are unconstitutional.

The first step was the ruling by U.S. District Court Judge Bernard M. Decker. He said the Second Amendment applies only to legislation enacted by the federal government, not state and local governments.

The amendment says: "A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed."

Decker, and later a state court, also rejected a state constitutional challenge to the Morton Grove law.

San Francisco Mayor Feinstein's proposal, which has not yet been introduced, is patterned after Morton Grove's, according to her criminal justice adviser, Rotea Gilford. However, the proposal calls for a mandatory 30-day jail sentence for those convicted of violating the ordinance.

Unlike Morton Grove, San Francisco has a serious gun crime problem and the highest per capita homicide rate in California. Feinstein's predecessor, George Moscone, and a popular supervisor were slain in a handgun attack in 1978.

Gilford noted that there are believed to be more handguns than people in San Francisco: 700,000 handguns and 640,000 people. "People are lined up at the stores to get them now. There's a six-month waiting list."

NRA officials say California state law preempts local gun control efforts, as do laws of Maryland and many other states, and thus local efforts in those states will be struck down in court. The Maryland General Assembly is considering a bill that would remove the preemption provision.

Anti-gun groups in California also are working to place an anti-handgun initiative on the November ballot. The proposal would require all handgun owners to register weapons and, after April, 1983, forbid purchase of new ones.

Lashford, the NRA official, said he believes his organization's membership has been reinvigorated by the rash of proposals. "We're flooded with calls," he said.

And Gilford said the experience in San Francisco over the past few days confirms the continuing vigor of those opposing gun controls. "We've been inundated with calls," he said. "They're all saying the same thing, like it's memorized, about the Second Amendment."

He said Feinstein was confident that the legislation would pass, however.