A deep rift opened in the European Economic Community today when its leaders ended their summit meeting here in angry deadlock over Britain's relationship with the other eight Common Market countries.

British Prime Minister Margaret Thatcher's attempts to prevent economically troubled Britain from paying considerably more into the EEC than it gets back in benefits were thwarted by her colleagues from the Continent, let by French President Giscard d'Estaing and West German Chancellor Helmut Schmidt.

They were willing to cut Britain's bill by only a third, which Thatcher curtly refused during tense negotiations that dominated the two-day summit meeting. Before they will give Britain more, France and West Germany want cooperation from Britain in the production and pricing of North Sea oil, fishing rights in British waters and the export of cheap British farm products. They agreed only on continuing the argument at another summit, possibly as soon as February.

The rift grows out of a central problem for the Common Market: the centrifugal forces of the national interests of its members still threaten to pull apart an increasingly united European community of nations.

Born of the vision that Europe could be built into a world superpower through the gradual integration of its nations' economies, super-power through the gradual integration of its nations' economies, currencies, laws and even governmental institutions, the EEC rapidly has outgrown the original Common Market of free trade.

It now has its own vast executive bureaucracy, elected international parliament, currency exchange system, agricultural and industrial aid programs, laws, regulations and courts to enforce them.

Its present nine-nation membership of Britain, Ireland, France, West Germany, Italy, Belgium, the Netherlands, Luxembourg and Denmark is to be expanded to 12 by adding Greece, Spain and Portugal.

But it suffers from growing pains. Most notably, its complex budgetary system for collecting money in special taxes and levies from member nations and then redistributing this money in agricultural and other subsidies has favored some rich nations and has hurt Britain, now comparatively poor. The system also has inflated food prices and created surpluses of milk, sugar and other farm products.

The British, who joined the Common Market late, after first snubbing it and then being blackballed by French President Charles de Gaulle, still are reluctant members. They see the EEC as a drain on their national budget, a cause of high food prices and a threat to British Sovereignty.

In recent opinion polls, a majority of Britons favored pulling out of the Common Market if Thatcher's demands for a refund of about $2 billion were not met. Britain's opposition Labor Party declared in Parliament today that it will campaign for withdrawal from the EEC, following the summit deadlock here.

But Thatcher promised today that Britain will stay in the EEC, because she believes that close European cooperation is vital "for what I call the Free World." She made clear, however, that she would disrupt the community, possibly trying to bring its institutions to a halt, if the British financial issues were not resolved.

In a remarkably combative post-summit press conference, Thatcher said the outcome was "totally unsatisfactory." She called the next summit "one last chance" for her demands to be met before she would retaliate by disrupting the EEC with British vetos as De Gaulle did during the 1960s.

Many Common Market country leaders were angered by Thatcher's aggressive, uncompromising and, in their eyes, undiplomatic attitude. Giscard d'Staing told French reporters that the British must learn to cooperate inside the EEC. A West German official said the British do not seem to understand that "to solve the problem of any one nation in the community we need a spirit of solidarity, a community spirit."

In the weeks leading up to the summit here, Thatcher typically had staked her political prestige in Britain on forcing the other EEC leaders to give in to her demands, which they regented.

"She was told here," one European diplomat said today, "that the others have political problems, too. If Britain pays less, somebody else is going to have to pay more."

"This is the fourth time we've met to discuss Britain's financial problems, which are to some extent home-made,' he added. "It's time to talk a bit down to earth."

Some Europeans blame Britain's problems on its own failure to modernize its industry to remain an effective exporter, while continuing to import too much from outside the Common Market. In part, Britain pays so much in custom levies in to the EEC because it imports so much from outside the community.

The current EEC president, Irish Prime Minister Jack Lynch, said today he had tried to "emphasize [to Thatcher] that the taxes and levies [for the EEC] don't belong to the national governments collecting them, but belong to the community."