London — ''Barbaric and pagan,'' say church leaders. ''Impractical - it just won't work,'' say many politicians, especially from the Labour, Liberal, and Social Democratic parties, and some Conservatives, as well as numerous judges and lawyers.
''Necessary,'' reply other Conservative members of Parliament, including Prime Minister Margaret Thatcher, as well as police union officials.
They are arguing, not about nuclear weapons or unemployment, but about another deeply rooted and sensitive issue in Britain: whether the crime of murder should be met by sentencing the offender to death.
Britain is almost alone in Western Europe in continuing to discuss the issue. It is about to come to yet another highly publicized vote on the floor of the House of Commons.
The Cabinet has decided that the vote should be held before the summer parliamentary recess at the end of July. Members will be free to vote their consciences rather than following party lines.
Although capital punishment for murder was suspended here in 1965 and abolished in 1969, sentiment to restore it has been reviving in recent years. Public opinion polls show a heavy majority of people in favor of it in cases of terrorists who kill, child murderers, and murderers of policemen.
The crime rate has been rising, and the use of firearms has grown at a rate that disturbs many. Some politicians link violence and crime to high unemployment, some to a breakdown in public morality, some to an overworked police force alienated from many young people in the inner cities.
The last test of parliamentary opinion was May 11, 1982, when the margin against restoration was 162 votes. At that time 111 of the Conservative Party's 332 MPs opposed restoration and 36 abstained. The Labour Party voted heavily against a return to hanging.
The closest votes were in cases involving terrorism or murder of police and prison guards. The vote showed that antihanging sentiment had increased since the vote before that one, which was in 1979.
But in the new Parliament, as many as half of the new Conservative MPs swept into Parliament in the June 9 general election are thought to favor capital punishment. An informal poll of MPs conducted last week suggests there will be 306 against and 300 in favor. But 38 MPs are either undecided or unwilling to say how they will vote.
''The new vote will be close,'' concedes one antihanging source who is close to the prime minister. But he said he would be surprised ''if a modern Parliament voted to restore the death penalty in Britain.''
Across the rest of Western Europe, this is a debate long since concluded. In France, West Germany, the Netherlands, Spain, and elsewhere, capital punishment has been abolished. Only in Turkey is it retained (as it is in the East bloc countries and in wide areas of the third world).
Yet on the right of British politics, support for capital punishment has never faded away, despite abolition in 1969.
''There's always been a part of public opinion swayed by the argument that hanging is suitable for those who kill a policeman or a prison officer in the course of their duties,'' a source close to Mrs. Thatcher says.
The campaign to restore the death penalty is led by Conservative MPs such as Eldon Griffiths, who wants the death penalty restored for premeditated murder and terrorist murder. This, he told the recent annual meeting of the Police Federation, would restate ''society's determination that it was not going to tolerate the deliberate slaughter of the innocent for political purposes or gain.''
Bound up in British attitudes is the terrorist campaign of the Provisional wing of the illegal Irish Republican Army (IRA).
Mrs. Thatcher's personal stand is that hanging should be available for egregious cases of terrorist and other kinds of murder. The Police Federation in Britain, whose members normally go about their jobs unarmed, wants the death penalty restored for all types of murder, leaving appeals for reprieve in the hands of the government.
Opposed to these views are clergymen such as the Rev. Amons Cresswell, new president of the Methodist Conference. He insists that taking another's life is morally wrong no matter what crime he may have committed.
Other opponents cite practical grounds. One professional judge told the Times of London that trials with death penalties as a possibility were always tense, and mistakes were more likely to be made. Northern Ireland Secretary James Prior says firmly that capital punishment would play into the hands of the IRA, allowing its members to believe they could become martyrs.
The Howard League for Penal Reform says a death penalty would be tragic if applied because of the risk of an error in prosecution. It warns against entrusting it to courts in Northern Ireland who try terrorists without juries.
Roy Hattersley, Labour Party spokesman on home affairs, says there is no evidence capital punishment actually deters crime.
If the Commons voted freely in favor of restoration, Mrs. Thatcher would probably introduce legislation some time early next year. Within her Cabinet, opinion is sharply divided on the issue. Mrs. Thatcher's line is accepted by Chancellor of the Exchequer Nigel Lawson, Employment Secretary Norman Tebbit, and Minister of Trade and Industry Cecil Parkinson.
Ranged against them are Northern Ireland Secretary Prior, Defense Secretary Michael Heseltine, and the leader of the House of Lords, William Whitelaw, who was home secretary in the last government. Five senior ministers are thought to be undecided.