The world's first international parliamentary election began today as voters in Britain, Ireland, Denmark and the Netherlands selected their representatives to the European Economic Community's first elected assembly.

After West Germany, France, Italy, Belgium and Luxembourg vote on Sunday, perhaps 100 million Europeans will have particpated in the election of 410 members of the European Parliament, the largely advisory legislative branch of the expanding Common Market.

Despite the European Parliament's present lack of real legislative power and general campaign apathy, both supporters and opponents of the Common Market believe that this election eventually may be seen as a decisive first step toward establishing an effective international government in Europe.

EEC policy on everything from trade and currency control to agriculture and defense is now decided by summit meetings of the leaders of Common Market member nations and councils of the nations' various Cabinet Ministers. Their decisions are carried out by the appointed EEC Commission and its steadily growing butreaucracy in Brussels. Disputes are settled by the European Court of Justice at The Hague.

The european Parliament, whose members also were appointed until now, has the power only to dismiss the entire 13-member EEC Commission, to order that its budget be held down to the previous year's level, to oversee its activities through legislative committees and to express its collective opinion through voted resolutions.

Observers believe that the European Parliament's opinion will carry much more weight, however, after its members have been elected democratically and include such relative political heavyweights as former West Germany chancellor Willy Brandt, leader of the Germans' Social Democratic slate and the combined socialists from the nine-member nations who are expected to form the largest party grouping in the new assembly.

The election also is expected to have an important domestic impact in several Common Market countries. In France, Gaullist leader Jacques Chirac is using it to test his strength against President Valery Giscard d'Estaing and Socialist leader Francois Mitterand. In Britain, Prime Minister Margaret Thatcher's Conservatives hope to follow their national election victory last month with an even more crushing defeat of the opposition Labor Party. In Denmark, opponents of EEC membership may demonstrate enough popular support to force another referendum that could take Denmark out of the Common Market.

The election is being spread over several days to accommodate member nations' electoral customs. Britain, Ireland, Denmark and the Netherlands are voting today to comform to the custom of weekday elections, while the other five are voting, as usual on Sunday. Greenland, now an autonomous Danish province, is voting on Friday. The method of voting ranges from geographic districts in Britain to nationwide proportional representation in France.

Today's ballots will be sealed until everyone has finished voting Sunday. Counting will begin after 9 p.m. Sunday with its progress broadcast on a Eurovision EEC-wide television hook-up. The final results will not be known until later next week.

Each of the four largest Common Market countries - Britain, West Germany, France and Italy - has 81 seats in the new elected Parliament. The other five have fewer seats.

Although Greece formally was admitted into the Common Market in ceremonies in Athens last week, it will not become a full member until January 1981. The EEC also has agreed on conditions for future membership for Spain and Portugal.

As voters appeared to be only trickling to the voting booths today, officials estimated that about 60 percent of those eligible would vote, well below traditional high election turnouts in four countries voting today. By contrast, only 56.5 percent of eligible voters went to the polls in the 1976 U.S. presidential election.

Former British prime minister Edward Heath, who took Britain into the Common Market in the early 1970s, completed a vigorous month of campaigning for the Conservatives in the European Parliament election by making an emotional final speech today.

"I can think of no greater step in the lifetime of our generation than today's historic election," Heath said. "Europe is making history and the world is watching us." Another Conservative former prime minister, Harold Macmillan, 85, also campaigned for the party today.

Because both the Conservatives and much of the Labor Party favor continued EEC membership along with a determined effort to win Britain a better deal financially in the Common Market, today's vote did not become another referendum on membership, as was once forecast.

Yet in Denmark, which stayed in the Common Market only after a referendum vote in 1972, anti-EEC felling is running high. Opinion polls showing 40 percent of the population against membership and another 20 percent undecided have led observers there to predict that half the new Danish delegation to the European Parliament may want to pull their country out of the EEC. CAPTION: Map, European Parliament, By Dave Cook - The Washington Post