With an evangelistic fervor that contrasted with the public feuding inside Britain's two major political parties, the new Social Democratic Party presented itself to the nation this week in a traveling party conference that sometimes resembled a religious revival.

Prolonged standing ovations for speeches by party leaders, emotional welcomes for new converts, and an almost complete absence of ideological argument characterized the conference's two-day stops in Perth, Scotland; Bradford, northern England; and London. "We're 21 today, 21 today," conference delegates sang in Bradford on Wednesday after five more Labor members of Parliament joined the Social Democrats, raising their parliamentary strength to 21.

The Social Democratic Party and the older Liberal Party, have joined in an electoral alliance as a centrist alternative to the governing Conservative Party on the right and the opposition Labor Party on the left. The alliance now has 32 members in Parliament. This is the largest representation for a third force in British politics in more than 30 years. However, compared to 336 Conservatives and 248 Labor members their strength remains slight.

The Social Democrats have attracted only one member of Parliament from Prime Minister Margaret Thatcher's Conservatives, despite Thatcher's record low performance rating in public opinion polls and growing public criticism of her economic policies by Conservative members of Parliament.

But Social Democrats pointed this week to a growing number of converts from the ranks of Labor and Conservative Party workers and a string of victories by the Social Democratic-Liberal alliance in scattered local elections. At today's party conference finale, one of the Social Democrats' four co-leaders, former Labor minister William Rodgers, challenged Thatcher to call a national election now, rather than wait until her government's term ends in 1984.

Earlier in the week the currently favored candidate for the Social Democratic leadership, former deputy Labor leader Roy Jenkins, argued that the new party should not be seen primarily as a spinoff from Labor or a reaction to Labor's ideological split. "We have a momentum of our own," he said. "We have a different and constantly growing constituency, and we give an equal welcome to those of different political backgrounds."

Such arguments are backed by opinion polls showing the Social Democratic-Liberal alliance gaining the potential support of two of every five British voters. But this week's conference still left the Social Democrats without a clear identity, economic policy or single party leader.

This is partly by design. Instead of the doctrinaire monetarism of the Thatcher government and socialism of the Labor opposition, the Social Democrats argued, they are preaching pragmatic improvement of Britain's mixed economy.

Although Jenkins declared today that the Social Democrats were "the true heirs" to the political radicalism that first built the welfare state, its only significantly radical policy is the adoption of proportional representation for future elections. Another Social Democratic leader, former Labor foreign secretary David Owen, acknowledged that this meant "openly advocating to the British people a coalition government system" in which no party would hold a majority in Parliament.

This is necessary, Social Democrats and Liberals argue, to eliminate violent political swings from left to right and back again.

The new party's four co-leaders and several other members of Parliament are among the most experienced British politicians, but some of the others apparently defected from Labor primarily because they were losing their local party bases. None of them have been elected as Social Democrats, so two upcoming by-elections for parliamentary seats vacated by the deaths of Conservatives pose important electoral challenges for the new alliance.