Former British prime minister Edward Heath has written to President Carter and the leaders of the five other western powers and Japan about to meet in Venice, warning them that no real progress in narrowing the dangerous gap between rich and poor nations is possible without a clear commitment from them to get the job done.

Heath was in Washington yesterday to testify before a House subcommittee on the next step in the so-called North-South dialogue between the world's industrialized and less-developed countries.

He also used the occasion to emphasize to American lawmakers the growing economic stake this country has in the stability of many of those potentially volatile poorer nations.

Heath was one of 21 members of a commission made up of leaders from industrialized nations and the Third World and headed by former West Germen chancellor Willy Brandt. The commission issued a major report in February that contained many recommendations for bridging the rich-poor gap in ways hopefully agreeable to both the have and the have-not nations.

The report has provoked limited discussion in the United States. Heath, an articulate spokesman for the group's work, has set out on a personal initiative to prod the West's leaders into actions that will "override the technical difficulties" of getting something done to defuse what he sees as an economic timebomb.

Attached to his letter to the western leaders are 14 initiatives that Heath believes are politcally and technically feasible to start and sustain.

He urged the leaders meeting in Venice to back at least one or two of these at the two-day summit that opens Sunday.

Heath argues that the measures unanimously recommended by the diverse Brandt commission suggest that there aren't other answers to the problem and that the western leaders must go through this sane process to understand fully that the problems of the generally, poor southern hemisphere are intertwined with those of the richer North.

The first of three main problems outlined by Heath yesterday concerns continued deterioration of the already "desperate payments situation" in the 29 or so least-developed countries and their lack of access to financial markets to ease these burdens.

While some of these countries may not seem economically important, many -- such as Somalia, Bangladesh and Sudan -- are of major strategic importance to the West and vulnerable to radical forces feeding off the economic problems.

The most urgent problem, however, lies among the more advanced developing countries such as Brazil, South Korea and Mexico, he said.

For example, Brazil is $50 billion in debt, $22 billion of that to commercial banks. It's interest bill alone on that dept is now larger than its total of $14 billion in exports last year.

There is a danger, Heath told the subcomiittee yesterday, that unless these countries are helped, at least one could default on its commercial loans with 12 to 18 months, with "grave danger" to the whole western banking system.

In an effort to dramatize the U.S. stake in such would-be calamities, and to help overcome the clearly negative mood in this country these days toward oversea aid programs, Heath noted that about 35 percent of U.S. bank claims on foreign borrowers are with less-developed countries. These claims amounted on $74 billion last July. For the countries most in debt, U.S. banks account for about 60 percent of commercial bank claims, he said.

Heath said that U.S. markets in these less-developed countries are larger than generally realized. In 1978, about 26 percent of U.S. merchandise exports went to such countries, outside of the oil-producing nations, which are considered a spceical category of developing countries.

One out of every 20 jobs here, he said, depends on manufacturing exports to the Third World, a trade that also result in a $14 billion surplus for that sector of U.S. international trade.

Tying this together in the name of global self-interest, Heath told the panel that the South has an "enormous demand" for goods that the North can produce, but no financial resources to pay, while the North has 18 million people unemployed and between $250 billion and $450 billion in unused industrial capacity.

But the industrialized world, even the successful German and Japanese economies, no longer have surpluses.

The surpluses -- an estimated $115 billion this year -- lie in the treasuries of the oil-exporting countries and more must be done to get them to use part of their surpluses to help less fortunate countries, Heath said.

The question, Heath said, is whether the oil producers will put their surpluses into financial aid institutions in their current form. If not, he argued, then the industrialized countries should be prepared to make some adjustments in those institutions, "and some seem justified."

A number of Heath's 14 points focus on this. He calls for greater effort to attract oil-producer surplus funds to the International Monetary fund, the World Bank and other international lending institutions. He also calls for giving the oil-rich countries decision-making powers within these institutions more closely related to the amounts they contribute.

Among the political needs for a more stable situation, Heath said the "single most important thing" would be settlement of the Palestinian issue which would reduce Arab suspicion of the West and make it easier for oil producers to justify maintenance of production levels to meet western needs.

Several initiatives are aimed at combatting world hunger. In 20 years, Heath told the subcommittee, the world population will expand by 50 percent, mostly in the poorer countries.

"The consequences of this" in terms of additional demand for food, raw materials and energy, he said "will be something that neither North nor South will be able to separate itself from."