Britain, the Common Market nation with the most at stake in future European Economic Community policy, appears to be the least engaged in the historic European Parliament elections in the nine EEC countries in early June.

Political interest was exhausted and campaign funds depleted by the national election here less than three weeks ago, and it is widely assumed that the victorious Conservative Party will easily win a large majority of Britain's 81 European Parliament seats in the voting June 7.

In addtion, what had seemed to be sharp, lively disagreements about Europe between the Conservative and Labor parties just a few months ago have since blurred. While the Conservatives are clearly more committed to the Common Market than the Labor Party, the Conservatives now present themselves as just as determined as Labor to fight for a better deal for Britain.

Although it is now one of the poorer Common Market nations, Britain has become the largest net contributor to the EEC budget. This is mostly because of the farm subsidies it pays as a food importer. In part, these subsidies are paying farmers in richer EEC countries for huge surpluses of milk, butter and other commodities.

Conservative Prime Minister Margaret Thatcher has pledged to work to reduce Britain's contribution, to eliminate the farm surpluses and modify the subsidy system, and to protect Britain's vital offshore fish stocks from depletion by the fishing fleets of fellow EEC members.

Theatcher's chancellor of the Exchequer, Geoffrey Howe, recently said in Brussels that he was "astonished" at the size of Britain's contribution to the EEC. He said the problem must be resolved this year. At a dinner she gave for visiting West German Chancellor Helmut Schmidt, Thatcher said that "we shall judge what British interests are" in the EEC "and we shall be resolute about defending them." She said, however, that this would be done within the context of a generally cooperative British approach to the EEC.

Although Thatcher had shown relatively little interest in the EEC in the past and some of her fellow rightists in the Conservative Party fear the EEC as a threat to British sovereignty, she has backed up her pro-European statements by putting pro-Europeans into key foreign policy positions.

The Labor Party, whose left-wing still wants to take Britain out of the Common Market, was more contentious toward the EEC while in power. According to the oft-told joke in Brussels, it was always obvious when Britain's Labor government delegation arrived because the whining did not stop when their plane's engines shut off.

Former Labor minister Anthony Wedgwood Benn, uncrowned leader of Labor's left, tried unsuccessfully to make the Common Market an issue in the recent election. He is now trying to whip up a vigorous anti-Common Market campaign for the European Parliament elections. Moreover, Labor's platform demands drastic changes that critics say would require a renegotiation or withdrawal of British membership.

On the other hand, former Labor prime minister James Callaghan is, as usual, trying to steer a neutral course. He wants to avoid making the Labor campaign seem like a second referendum on British membership in the EEC. Despite higher food prices and other problems that have been blamed on the Common Market, a majority of British voters have consistently favored staying in it.

The obvious friction between Callaghan, who was recently reelected as Labor's leader despite the party's election defeat May 3, and Benn, who has quit Callaghan's "shadow cabinet" to speak out more freely, is only one of several problems plaguing Labor in the campaign for the European Parliament election.

Because the vote follows on the heels of the national election so closely, the turnout may be as low as 50 per cent. This should mean a big drop in the Labor votes. In addition, Labor has no more money to speed on its European Parliament candidates.

As a result, the Conservatives are expected to win between 50 and 60 of the 78 European Parliament constituencies on the British mainland.

Perhaps because Labor's outlook is so grim, many of the European Parliament candidates are national political newcomers, a disproportionate number of them academics and journalists. Surprisingly, only one-third of them are strongly anti-European.

The Conservatives have fielded a much more experienced, older, and more prestigious slate of pro-European candidates.