LONDON, JAN. 22 -- The House of Commons today approved in principle a new law to reduce the legal limit for abortions in this country from 28 weeks of pregnancy to 18.

The vote marked the first potential rollback in the liberalization of abortion laws that began in several western countries in the mid-1960s.

The 296-251 vote gave an unexpectedly decisive majority to the measure, which has been the subject of heated campaigns by both pro- and anti-abortion lobbies here for the past several months.

The decision came as thousands of pro- and anti-abortion activists were demonstrating in Washington on the 15th anniversary of the U.S. Supreme Court decision legalizing abortion.

Britain's existing law, passed in 1967, is one of the world's most liberal. Under its broad provisions, hundreds of thousands of foreign women have traveled here for abortions over the past 20 years from countries where abortion is illegal or more strictly limited. There have been at least a dozen previous attempts to narrow the British law.

Liberal Party legislator David Alton, a Roman Catholic who introduced the measure as a "private member's bill," indicated in the face of strong opposition during today's debate that he would be willing to consider amendments to increase the 18-week limit, and to allow later abortions for women found to be carrying handicapped fetuses.

That pledge seemed to assuage a number of legislators who, while considering 28 weeks too long, had argued that an 18-week limit would effectively bar abortion for those women who had undergone amniocentesis, a procedure to identify certain fetal abnormalities, like Down's Syndrome. The test cannot be performed until the 16th week of pregnancy, and it takes four weeks to determine the results.

Other opponents of the bill said they did not trust the pledge, and warned that it would be considered a victory that could not be altered without a fight by antiabortion forces.

They insisted that if the 18-week limit were not extended to at least 24 weeks the bill would not be approved in a final vote, which must be held by July.

Members were authorized to vote their consciences today, rather than a party line. Prime Minister Margaret Thatcher, who did not appear for the vote, said yesterday that she was opposed to the change. Her office indicated that she preferred a limit of 24 weeks, the age at which a 1985 report by the Royal College of Gynecology determined a fetus is viable.

Although public opinion polls consistently have shown that most Britons favor legal abortion, recent surveys have indicated support for lessening the 28-week limit, with 40 percent saying they approve of 18 weeks.

In practice only 3.3 percent of the 170,000 abortions performed here last year were after the 18th week of pregnancy.

The U.S. Supreme Court ruled in Roe vs. Wade in 1973 that the states may not prohibit an abortion during the first three months of pregnancy. During the second three months, abortions may be regulated solely to protect the woman's health. The ruling was reaffirmed in 1983.

Alton's bill was supported by the 30,000-member Society for the Protection of the Unborn Child, which over the past several weeks has mailed out thousands of posters and postcards picturing an 18-week fetus sucking its thumb in the womb.

The society also has sponsored showings of U.S. physician and producer Bernard Nathanson's videotape "Eclipse of Reason," the sequel to his "Silent Scream," a film allegedly depicting pain felt by a fetus during an abortion.

"By 18 weeks, a baby, a fetus, is not just a clump of tissue or a blob of jelly," Alton said during today's debate. "The child has sentience. It can feel pain . . . It has a complete skeleton. It has reflexes" and "could be in agony during abortion."

But in one of many other emotional statements, Conservative member of Parliament Andrew Mackay opposed the bill.

"All I can say to the House is that my wife and I are not sufficiently capable as parents to have a disabled child," Mackay said. "I'll be totally honest with you, I could not cope with it. I have terrific admiration for those wonderful people who are able to cope. But the decision must be theirs, it must not be ours."

After passage on second reading, a bill is referred to a committee where it is discussed and possibly amended before being presented to the House for a final vote.

While not final, the stage which the Alton bill passed today is the most crucial and is the point at which new laws generally are accepted or rejected. One of the most ardent opponents of the Alton bill was Liberal Party leader David Steel, who as a junior member 21 years ago shepherded through the current broad law, legalizing abortion up until the moment of "fetal viability."

Its provisions require certification by two doctors that the risk to the life or mental or physical health of the woman, or her existing children, would be greater if the pregnancy were to continue than if it were terminated.

Viability, at the time, was determined under a separate, 1929 act that set the limit at 28 weeks.

In the early years of the 1967 law, before the U.S. Supreme Court ruling, thousands of American women flew to Britain to obtain abortions, as did women from many other countries until the procedure was legalized in most of Western Europe. Laws permitting abortion, generally in the first trimester of pregnancy, now exist in much of Western Europe, and even with an 18-week limit Britain would remain among the most liberal.

The largest number of foreign women seeking abortion in England and Wales now come from Spain and Ireland, where the procedure is illegal.

The overwhelming majority of a total 170,000 abortions performed here last year took place long before the 28-week currently allowable limit. Only 49 were performed on women who had passed the 24th week of pregnancy.

Since the 1985 Royal College of Gynecology report, which said that medical advances had meant that fetuses as young as 24 weeks can live outside the womb, it has been de facto policy that any abortion past that time must have government approval.