Rapidly changing opinion polls, a by-election result and the assassination of the Conservative Party's spokesman on Northern Ireland have clouded the opening of Britain's national election campaign.

The most recent public opinion poll, taken after Prime Minister James Callaghan's Labor Party government was brought down Wednesday by a no-confidence vote in the House of Commons, indicated that the opposition Conservatives' big winter lead over Labor has been halved.

According to Market and Opinion Research International, whose poll results have been roughly paralleled by the Gallup surveys here, the 19 per-cent lead the Conservatives opened up over labor in February, in the midst of a weary winter of bad weather and frequent strikes, fell to 13 percent in March and just 9 percent most recently.

With less than five weeks left before the May 3 election, polling experts expect that margin to narrow further in a bitter, expensive campaign.

The murder yesterday of Conservative member of Parliament Airey Neave, which took from Conservative leader Margaret Thatcher one of her closet parliamentary and campaign advisers, has postponed the public start of the campaign. Thatcher canceled an address to have been nationally televised last night and Callaghan postponed a radio broadcast today. Other weekend political speeches across the country wer put off.

The assassination of Neave in the explosion of a car bomb just outside the house of Commons, for which terrorist factions of the Irish Republican Army have claimed responsibility, has also greatly increased concern that IRA terror may strike again during the campaign.

Scotland Yard announced today that security was being increased at Parliament's Westminister Palace for a large number of Labor government ministers and their Conservative counterparts.

The IRA singled out Neave, who would have been Northern Ireland secretary in a Thatcher administration, because of his outspoken opposition to withdrawal of British troops from Ulster.

The IRA had vowed to force the Northern Ireland question to the fore during the campaign through violence. It began with widespread bombings in Ulster and the murder of the British ambassador in the Netherlands.

Reaction to Neave's murder, however, has reinforced a unity of purpose between the Labor and Conservative parties on Northern Ireland. They are agreed that British rule, with emphasis on security, remains necessary to prevent even more bloody sectarian violence in Ulster and that no political solution can be tried without the full support of both the Protestant majority and the Catholic minority.

Neither major party expects to win any of the ulster seats in Parliament, most of which are held by Protestant Ulster Unionists. But elsewhere in Britain, the success that the Conservatives and Labor have against other minor parties could determine which will gain a majority of the seats in Parliament and hence control the government.

The liberal Party, which had fallen in popularity after winning 1o Commons seats and 20 percent of the vote nationwide in 1974, has won encouragement from a by-election Thursday to fill a vacant seat in Liverpool.

The winning Liberal candidate, who amassed 65 percent of the vote in the small, lower-income constituency, will serve in the outgoing Parliament for only a week before it is dissolved next Saturday.

But the Liberals' leader, 40-year-old David Steel, called it a "stupendous result" that indicates "there is going to be a significant wedge of Liberals in the next Parliament." The victory was a vindication of Steel's strategy to concentrate the Liberals' resources on just 20 to 40 constituencies where they have the best chance of winning.

Because the Liberals fit between tne Labor left and the Conservative right, they attract swing voters who-if they decide not to vote Liberal-could help provide the margin of victory for either of the major parties.

A problem of unknown proportions facing the Liberals in the May 3 election is the candidacy of their former eader, Jeremy Thorpe. His trial on charges of conspiring to murder a man who claims to have been his lover is scheduled to begin April 30, just days before the election.

Thorpe, who is credited both with using his charisma and an effective media campaign to boost the Liberal's vote in 1974 and with helping to cause the party's subsequent decline when lurid details of his criminal case were made public here, announced tonight that he nevertheless will stand for reelection to his seat in the House of Commons.

In Scotland, the success of the two major parties is similarly contingent on the strength of another minor party, the Scotish Nationalists. They rode to victory in 11 parliamentary constituencies in Scotland in 1974. A steady decline in the Scottish Nationalists' standing in opinion polls since then had given Labor and the Conservatives hopes of recapturing some of those seats.

But the outcome of the home-rule referendum in Scotland earlier this month has confused the picture. The proposed Scottish assembly was approved by only a bare majority of those voting and only a third of the registered voters in Scotland. Since the Conservatives had campaigned hard for a "no" vote, they seemed to have come out of it best, while the Labor government, which strongly backed the plan, was embarrassed.

The size of the "yes" vote, however, would still be sufficient to return many of the 11 Scottish Nationalists to the House of Commons.

The Scottish Nationalists will be campaigning against the failure of the Labor government to implement home rule for Scotland, which is what finally led to the no-confidence vote against Callaghan.

Polling experts said either Labor or the Conservatives could win by a 3 percent margin of the popular vote and achieve a majority of 20 or more seats in Parliament. But they also warned that the demise of the minor parties may have been exaggerated and voters may not be ready to swing sharply in one direction or another, which could leave either Labor or the Tories barely in control of Parliament and facing more of the uncertainty that plagued Callaghan.