President Carter leaves Washington for London today and his first brush with personal diplomacy at a summit conference.

In a crowded, five-day schedule, the President will tour northeastern England, attend a two-day summit conference on economic and related issues in London, fly to Geneva for a brief meeting with President Hafez Assad of Syria and return to London in time tfor a meeting of the North Atlantic Treaty Organization on Tuesday.

Moreover, the Presidtn has already given the trip his own brand, slashing the size of the American contingent as a cost-cutting measure.

The economic summit confernce Saturday and Sunday, the third such session since 1974 among the leaders of the United States, Western Europe, Canada and Japan, is the centerpiece of Carter's first trip overseas as President. But in all liklihood it will be the new American President himself, still something of a mystery to the other government heads and their countrymen, who will be the center of attention.

Neither of the previous economic summit conferences produced dramatic developments, and American officials have said they do not expect the London meetings to differ in that respect.

But they will provide Carter and the leaders of the United States' most important allies with a chance to get to know each other better and to foster greater cooperation on international economic issues administration officials say.

Subjects to be discussed at the summit include trade, th energy shortage that afflicts all of the participating nations and aid to the developing nations. The President is likely to encounter skepticism in London over whether the U.S. economy is expanding rapidly enough and over his attempts to stem the tide of nuclear fuels to non-nuclear nations.

Other participants in the meeting will be British Prime Minister James Callaghan, West German Chancellor Helmut Schmidt. French President Valery Giscard d'Estaing. Italian Prime Minister Giulio Andreotti. Canadian Prime Minister Pierre Elliot Trudeau and Japanese Prime Minister Takeo Fukuda.

Carter, who will leave Andrews Air-Force Base at 10 a.m. today, will be accompanied by Secretary of State Cyrus R. Vance and Treasury Secrtary W. Michael Blumenthal. But Carter, concerned about the costs of transporting the American party to Europe, personally slashed a number of policy-making officials from the trip.

As a result, although there were a total of 83 "priority requests" to make the trip, the U..S, contingent will number about 60, exclusive of security, trnasportation and communications personnel.

According to a White House official, two aides have worked almost full time this week hearing appeals from those destined to be left behind and monitoring cable traffic to detect officials planning to show up in London anyway. Such officials were told not to come.

The Carter style also surprised U..S embassy officials in London, who had booked the American party into Claridge's, one of the poshest hotels in Europe and a favorite offormer Secretary of State Henry A. Kissinger. They were told to switch the reservations to the less expensive Britannia Hotel.