Britain's opposition Conservative Party enters the campaign for the May 3 national election with a comfortable lead in public opinion polls and with its leader, Margaret Thatcher, at an all-time high in personal popularity.

Two opinion polls taken early this week, after the Labor Party government of Prime Minister James Callaghan was brought dwon by a vote of no confidence in the House of Commons, showed the Conservatives lesding Labor by 13 to 15 percentage points.

At the same time, Thatcher, who has always trailed her own party in the polls, made her best showing yet. She ran virtually a dead heat with Callaghan on the question of "who will make the better prime minister" in the poll taken by Market Opinion and Research International, which is also Callaghan's private polling firm.

Its poll also showed Thatcher receiving a strongly positive rating on her performance as opposition leader, while Callagan was rated negatively on his performance as prime minister. A larger than normal percentage of voters who remained undecided on both Thatcher's job performance and her potential as prime minister represents the swing vote that is expected to decide the election.

With her strong position in the polls, Thatcher turned down an invitation by Britain's commercial television network to participate in two American-style televised debates with Callaghan and the Liberal Party leader, David Steel. Callaghan and Steel had agreed to the debates.

Thatcher said in a letter to the network that she had refused because "I believe that issues and policies decide elections, not peronalities. We are not electing a president, we are choosing a government."

Her response reflected the fact that in both of this week's opinion polls voters selected as the most important issues those that Thatcher already emphasized in speeches launching her campaign: inflation, taxes, trade union power, and law and order. Strong majorities of the respobdebts in both polls said they believed the Conservatives were better able than Labor to cope with each of these problems.

Thatcher's strongest campaign promise so far is an immediate, sizable cut in income taxes if the Conservatives take power, a promise she emphasized in a nationally televised speech this week. Labor began to respond yesterday when the outgoing chancellor of the exhequer, Denis Healey, told Parliament that if the Labor government had not fallen he would have included significant tax relief in his new budget.

Thatcher has not yet outlined specifics on how she would hold down inflation, control labor unions or curb crime. The Conservative plan a low-key campaign in which Thatcher will make quick campaign trips out of London by jet and will try to avoid confrontations with Callaghan.

Labor will be running as the party with the most government experience in recent years, having been in power 12 of the last 15 years, and as the party that cares most about the only other issue considered important by opinion poll respondents - unemployment. Callaghan will try to draw out Thatcher and show her to be inexperienced in governing and unrealistic in approaching the country's problems.

The vast majority of voters here support the same party year after year - upper-income, middle-class and rural voters favoring the Conservatives, lower income, union member and urban voters favoring Labor. The outcome of the election will be determined by only 10 to 20 percent of the voters in about 100 closely contested parliamentary constituencies of the more than 600 across the country.

Polling experts believe this swing will be most influenced by two over-riding factors: the state of the economy and the voters' perception of Thatcher as a national leader.

This week's polls show that labor trouble had receded somewhat as an issue after a winter of strikes here. Many unions, representing hospital workers, ambulance drivers and local government workers among others,have finally settled on new contracts with pay raises.

But other workers, including the nation's civil servants, are still engaged in selective strikes that have slowed the handling of mail in London, forced prisons to keep inmates locked up in their cells around the clock, idled government computers, and periodically created long lines at customs and immigration posts at ports and air terminals. CAPTION: Picture, MARGARET THATCHER ...personal popularity high