IN THE SUMMER of 1956 the streets of Cairo were filled with long snaking lines of chanting demonstrators carrying banners denouncing the British. The Americans, the Israelis and many of the leaders of the Arab world.

Egypt's Gamal Abdel Nasser had just seized the Suez Canal and, while the great wartime powers met in London to decide what to do, Cairo danced with joy. One vivid poster at the time showed preposterous cartoon faces of Western leaders having their noses tweaked. John Foster Dulles could choke on his own bile, Nasser told his excited populace.

Twenty-one years have passed since that emotionally overheated summer - my last opportunity to report from Egypt - and that particular wave of Arab nationalism that Nasser both represented and rode so well has crested and receded.

Three wars with Israel have taken place since that summer, all of them fought on Egyptian territory in the Sinai. In 1956, Israel needed help from the French air force flying from Israeli bases to mount its campaign in the desert. Today, the Israeli air force is bigger than the French and British air forces combined.

SEEING EGYPT'S PRESIDENT Anwar Sadat with Secretary of State Cyrus Vance in Alexandria this month and listening to him describe his trust in the United States to find a solution to the Middle East problem, it is hard to imagine that earlier summer or conceive how radically Sadat has changed the course of Egypt's foreign policy.

Whereas Nasser took Egypt out of the Western camp into the Soviet orbit in his effort to rid the Middle East of the last vestiges of European colonialism, Sadat has reversed this policy. He has removed Egypt from the Cold War and put it back in the American sphere of influence. Indeed, it is startling to see how much he has mortgaged his politics to the Americans in the hope of a Middle East settlement and how much he needs and equitable settlement with Israel to survived the domestic and economic troubles that threaten to overwhelm him.

Coming to Egypt from Israel, one is immediately aware of the misconceptions each has of the other and the hugeness of the gulf over which the dumb are shouting to the deaf. The Israelis still largley believe that, no matter what is said, the Egyptians still mean to do them in - that the talk of peace is, in the long run, "another tactic to get a little closer to our throats," as one Israeli leader put it.

In Egypt, however, one gets the impresssion that the Egyptians, although not particularly happy with the Jewish state, are ready to come to a peace agreement and would go to almost any lengths, short of complete humiliation of the Arabs, to put the entire Arab-Israeli struggle behind them.

THE MAJOR CONCERN of Egypt today, as one official put it, is "to solve the crushing gap between our expectations and our fulfillment." Continuation of the Arab-Israeli confrontation is simply dragging Egypt deeper into the mire.

Egyptians seem to have outgrown the anti-Israeli obsession so much in evidence 20 years ago. Egypt appears willing to settle if the Arabs can have back what they lost in the 1967 war. The Israelis, who never originally intended to keep the spoils of the that six-day war, have now grown comfortable with the extra breathing room and are loath to give it all back for a scrap of paper that may or may not mean a lasting peace.

Many Egyptians see Israel as a state committed to keeping the Middle East conflict alive - a garrison state that needs outside threats to solve its own internal contradictions and to keep foreign contributions flowing into its coffers. The Egyptians sometimes misunderstand . . . and mistake for arrogance . . . the deep fear of the Israeli that once again the Jews could face extinction. Egyptians see the most powerful military machine ever assembled in the Middle East and cannot understand the insecurities of those who wield it.

Another potentially dangerous misconception is the idea in Egypt that, if only the United States really wanted to, it could force Israel into line overnight. If the United States has learned anything in the last 20 years, it is that the client-state tail can often wag the American dog; no matter how much Israel may depend on the United States, there are limits to the pressures, the Americans can bring to bear; and a stubborn Israel backed to the wall could bring down the whole structure like Samson at Gaza.

WHAT OF THE city of Cairo itself? The years have not been kind and, with a population swollen to more than eight million, the city seems to be breaking at the seams as public transportation and services fall apart. But Cairo still has an elegance and style that is not to be found in any other Arab capital.

The great River Nile no longer roars boiling through the city in flood season, as it did before the hgih dam at Aswan was built. It resembles more the Seine in its placidity.

Although there have been obvious improvements for the people - for example, one no longer sees so many people with eye diseases - the crowding and poverty are, if anything, worse.