The House of Commons' solid rejection of capital punishment in murder cases Wednesday night climaxed a lively, month-long national debate on the issue that displayed the best of British democracy in action.

The opposing sides in the country at large aired their views in a stream of resolutions, newspaper articles, radio and television programs and curbstone discussion. The Church of England synod stood firmly opposed, along with prison wardens and even several former executioners. The police federation was in favor, as were relatives of murder victims.

"When Susie died," wrote the mother of an 11-year-old murdered last summer, "we received over 2,000 letters of sympathy from all over the country, and hundreds of people told us they felt hanging to be right in such cases."

What characterized the arguments was their intensity and recognition of the fact that--in contrast to the experience in the United States, where authority is fragmented--sentiment would be tested quickly in Parliament.

Within days after the country's general election in June, optimistic proponents of hanging had arranged for a vote on the issue as one of the first items of business in the new House of Commons. More than at any time since abolition of the death penalty in 1965, the climate seemed right for Britain to join other countries, including the United States, that have resumed or increased executions in recent years.

The enhanced parliamentary majority of Conservative Prime Minister Margaret Thatcher--a supporter of capital punishment--suggested that the political mood might have shifted to the right on this issue as on others. More than 100 new Tory members of Parliament could be counted on, the hanging lobby believed, to swing the margin narrowly in favor of "bringing back the rope."

Many of these fledgling lawmakers had promised their constituents during the campaign that a tougher stance on crime, including the restoration of murder as a capital offense, would be a major feature of coming legislation. Moreover, the continued activities of terrorists in Northern Ireland provided considerable support for the argument that the death penalty is essential as a deterrent.

Although the government takes no formal stance on capital punishment (members of Parliament were freed from party discipline to vote on the issue as a matter of conscience), Thatcher's new home affairs minister, Leon Brittain, let it be known that he would endorse the death penalty in cases of terrorism.

Nevertheless, the newspaper headline that read "Hanging--it may be yes" turned out to be wrong--by a wide margin. The vote against the death penalty Wednesday was about as large as it was in 1979, at the start of the last Parliament, when the Conservative majority in Commons was roughly half of what it is now.

With most opinion surveys showing a plurality in favor of hanging in aggravated murder cases, Parliament's judgment seemed at first glance to be defying the wishes of the electorate. But what really happened, it seems, is that the opponents of capital punishment, in a fair fight with the supporters, won the argument.

In the week before the vote, according to Nicholas Comfort, political correspondent of the Daily Telegraph, mail to members of Parliament dramatically shifted to about 5 to 2 against the death penalty. The more closely the new members examined the issues and discussed them with the voters, the more complex they found attitudes to be.

One new member voted on different sides on seven resolutions because, he concluded, no general principle on capital punishment could be sufficiently well-designed to provide necessary safeguards.

In short, while public sentiment for retribution against murderers remains strong, a majority in and out of the House of Commons decided that hanging is not the solution.

As another outcome of the debate, there is likely to be broader support for lengthening prison terms for certain categories of crime; for instance, making a minimum 20-year term mandatory for shooting a police officer.

Finally, what was said in Wednesday's parliamentary exchanges had its effect. There were about 40 speakers in about six hours. Brittain, who made the main speech in favor of hanging for terrorists, did poorly, it was generally agreed. The case against hanging, on the other hand, was put persuasively by such former senior ministers as Edward Heath and Roy Jenkins.

In the best traditions of British debating societies, when the votes were called, the side with the greater eloquence won the day.