Despite stalemate and rancor in the Palestinian autonomy talks, Egypt is moving ahead with unexpected speed in setting up the normal bilateral relations with Israel outlined in their 13-month-old peace treaty.

Far from the theater of visits to Washington by President Anwar Sadat and Prime Minister Menachem Begin, Egyptian and Israeli diplomats negotiating smoothly and without fanfare in Cairo and Tel Aviv this week signed the last of eight accords designed to transform the two former enemies into good neighbors.

This marked a three-month advance over the timetable foreseen in the March 26, 1978 treaty. The swift agreement underlined Sadat's policy of separating progress in the normalization measures, where both sides want basically the same thing, from progress in the autonomy talks, where each side wants something vastly different.

The Egyptian leader's willingness to proceed on this basis, often against the advice of his own Foreign Ministry specialists, has been crucial in allowing negotiators to set up the framework for normal relations ahead of schedule. Barring swift progress in the autonomy talks, however, it also has left Sadat exposed to charges that his Arab critics were right in accusing him of making a separate peace with Israel.

The final accord, regulating commerce and trade, was signed this weekend in Cairo just before a reception in a hotel overlooking the Nile to mark Israeli independence day. It had been preceded by accords regulating Egyptian oil sales to Israel, telephone and postal service between the two countries, transports, tourism, agricultural cooperation, cultural exchanges and civil aviation.

"I have been involved in the peace process almost from the beginning, and I never imagined we would be this far by now," said Yousef Haddass, an Arabic-speaking Syrian Jew who is the number two man at the Israeli Embassy here under Ambassador Eliahu Ben-Elissar.

The Israeli reception, Ben-Elissar's first venture of such scale on the Cairo circuit, also was a milestone in its own way. It was attended by a sprinkling of Egyptian officials and, to the surprise of many observers, Minister of State for Foreign Affairs Butros Ghali.

Ghali, who has urged a closer link between the autonomy talks and bilateral progress, reportedly had been encouraging his Foreign Ministry officials to keep their distance from Ben-Elissar and his embassy staff. Ghali's appearance at the reception thus was taken as a signal that the ministry's unofficial social boycot is softening.

The Foreign Ministry still can control the spigot of normalization, however, because the eight accords provided for in the treaty form only an outline for normal relations. The Egyptian bureauracy could prevent or delay concrete steps if Sadat decided later to reduce the flow to make a point in the autonomy talks.

At the same time, many of the concrete steps already have been carried out. The first private business deal resulting in delivery of Israeli merchandise directly to Egypt became a reality last week when 10,000 chicks arrived at Cairo airport in the hold of an El Al plane -- and got such swift service by the clearing agent that they left the airport before passengers who had arrived aboard the same flight.

El Al officials report their twice-weekly flights between Cairo and Lod Airport near Tel Aviv operate at about 90 percent of capacity. Nefertiti, the Egyptian airline formed last month specially for the Cairo-Lod run, reports about 60 percent of capacity on its flights, also twice a week. Diplomats say both airlines are considering adding a third weekly flight for what is expected to be steadily improving business as tour agencies schedule visits combining Egypt's historical monuments with the Holy Land.

Since last week, tourists also can travel in private cars between Israel and Egypt. Travel by bus or taxi has been possible since late January through a gate at El Arish, an Egyptian town marking the northern end of the withdrawal frontier until April 1981.

The traveler who makes his schedule fit the timetable for crossing the Suez Canal can take an Egyptian taxi to El Arish for about $7.50 and then pick up an Israeli taxi on the other side for a $10 ride into Tel Aviv. A one-way plane trip costs $85.

Most travelers have been foreigners. But Egyptian authorities have issued about 5,000 visas to Israelis since visits began last July, 2,000 since the Israeli Embassy opened here Feb. 18.