What was going on when I was born?

The two-party dominance of British politics, which has endured since World War II, seems in serious jeopardy. If Labor and the Conservatives are to maintain their monopoly on power, both will have to regroup rapidly. To a political community already dazed by the most rambunctious round of party conferences in two decades, the startling result of a by-election yesterday in the obscure dormitory town of Croydon, south of London, administered a further shock. The election was won by William Pitt, a perennial loser, as the parliamentary candidate of the Liberal-Social Democratic alliance, which came into existence only in the last few months, in a constituency where third parties have never mounted any real threat. It raises the possibility that Shirley Williams, a former Labor Cabinet minister, may soon return to the House of Commons as an alliance member through a by-election at Crosby, near Liverpool. Before the result at Croydon North West was announced early this morning, nobody had given Mrs. Williams much chance of overturning the majority of 19,272 amassed by the Tories at Crosby two years ago.

A gunman was killed and a second was captured in a high-speed chase and shootout in Queens yesterday after the police linked their car's license plate to a gang that killed two policemen and an armored-car guard Tuesday. It was unclear whether the two men were among the four to eight gang members who escaped after the $1.6 million Brink's armored-car robbery and the shootings in Nanuet and Nyack, in Rockland County. But authorites said there were indications that the men were linked to the robbers. The slain man may have been wanted for assaults on police officers, the police said, and the captured man was identified as a former Black Panther once charged in a bombing plot. In Nyack, the four suspects who were seized after the holdup were arraigned in handcuffs yesterday amid extraordinary security in the Rockland County village 20 miles north of New York City.

The Polish Government announced today that it was sending teams of troops throughout the country to resolve unrest. The action came hours after Solidarity, the independent labor union, called a Excerpts from statement, page 5. one-hour national strike for Wednesday to protest food shortages and what it called harassment. A statement, read over television by the Government's spokesman, Jerzy Urban, said the soldiers would be empowered to ''counteract problems on the spot'' and would attempt to ''solve problems and controversies.''

114 TOXIC WASTE SITES LISTED AS NATION'S MOST DANGEROUS WASHINGTON, Oct. 23 (By The Associated Press) - The Government ranked 114 hazardous waste sites today as the worst in the country in the start of a $1.6 billion attack on poisonous chemicals that threaten health and the environment. The list, prepared by the Environmental Protection Agency, will be used to disburse Federal money under a program established by Congress last year to clean up dangerous waste dumps. Thirty-nine states placed sites on the list, which was compiled from a group of 282 sites nominated last summer by the states and regional offices of the environmental agency. The dumps were rated on the basis of their potential danger to health, primarily to drinking water supplies, with threats to the environment also taken into consideration. The 11 states that did not apply to have dumps listed were Alaska, Hawaii, Idaho, Louisiana, Montana, Nebraska, Nevada, Vermont, Oregon, Wisconsin and Wyoming.

A Federal agency today abandoned the longdisputed requirement that automobile manufacturers install automatic crash protection, such as airbags or ''passive'' safety belts. The action by the agency, the National Highway Traffic Safety Administration, drew immediate protest from safety groups and praise from the automobile industry. The decision was part of the Reagan Administration's regulatory review. Raymond A. Peck Jr., head of the safety agency, said the crashprotection standard was rescinded because the agency had concluded that car owners' past practices with manual belts indicated that they would disconnect the ''passive'' seat belts. Those belts wrap around a driver automatically as he closes the car door.

Leaders of 22 industrial and developing nations ended two days of closed-door talks tonight without a major breakthrough in their longstanding differences. The leaders reached a provisional accord to pursue development negotiations at the United Nations, but despite the hopes of some third world countries they were unable to agree on the terms or the date for the new talks. A statement read tonight by the conference's co-chairmen, President Jose Lopez Portillo of Mexico and Prime Minister Pierre Elliott Trudeau of Canada, merely noted that the leaders had ''confirmed the desirability of supporting at the United Nations a consensus to begin global negotiations on a basis to be mutally agreed and in circumstances offering the prospect of meaningful progress.'' Mr. Lopez Portillo stressed that the conference, attended by President Reagan as well as leaders from Britain, France, Japan, China, India and other countries, ''was a forum for creating awareness and expressing political good will and not for reaching concrete agreements.''

The Consumer Price Index, pushed up by increases in food, transportation, interest rates and medical care costs, surged 1.2 percent in September. At an annual rate, this comes to more than 14 percent. The September increase in the nation's most widely followed measure of inflation meant that consumer prices have been rising at a double-digit annual rate since July, when the index also jumped 1.2 percent. It rose eight-tenths of 1 percent in August.

A Federal indictment was made public today accusing a 38-year-old Virginian of shipping explosives to Libya and training terrorists there as part of a conspiracy headed by two former Central Intelligence agents. The 10-count indictment also broadened the charges against the two former agents, Edwin P. Wilson and Frank E. Terpil, to include a shipment of explosives to Libya in April 1977. The last shipment listed in the original, April 1980, indictment of Mr. Wilson and Mr. Terpil on the explosives charges took place in August 1976. The charges against the new defendant, Douglas M. Schlachter Sr., grew out of the testimony of ''newly cooperating witnesses,'' according to Carol E. Bruce, one of the assistant United States attorneys working with the grand jury investigating the Libyan venture.

Greece's new Socialist Government announced today that it had decided to upgrade the diplomatic status of the Palestine Liberation Organization office in Athens but that its exact level would be determined later. Prime Minister Andreas Papandreou invited Yasir Arafat, the head of the P.L.O., to visit Athens to discuss the issue. Earlier, a Government spokesman said that the P.L.O. office here would be raised to the level of an embassy in accordance with pledges made during the recent election campaign. But a Cabinet meeting was then held, and later there was no longer any talk of full diplomatic recognition.

Pope John Paul II has appointed a conservative Italian theologian to take over direction of the Jesuit order as his personal ''delegate'' until the order elects a new leader. The Pope's move, which was announced by the Jesuit headquarters here in a short statement today, will greatly strengthen the Pope's control over the traditionally independent Society of Jesus, Vatican sources said. In a letter to the Rev. Pedro Arrupe, the Jesuit leader, who suffered a stroke in August, the Pope said the appointment of Father Paolo Dezza was meant ''to represent me more closely in the society.''

The Speaker of Iran's Parliament said today that the Islamic Government had succeeded in destroying most of the guerrilla forces opposing it and had cut the rest off from their leaders abroad. This statement appeared to be the most emphatic proclamation by an Iranian leader so far of victory over the leftist guerrilla organization People's Mujahedeen, whose chief, Massoud Rajavi, is in exile in France.

President Hosni Mubarak said today that the assassination of Anwar el-Sadat was the first and key step in a plot to topple the Egyptian Government and install a fundamentalist Moslem regime modeled after that of Iran. In an interview with the semiofficial newspaper Al Ahram, to be published tomorrow, Mr. Mubarak said the assassins and their supporters intended to create national havoc after killing Mr. Sadat and other political, military and religious leaders and seizing key Government centers and communications installations. The takeover of the Government, the President said, was to be accomplished during the national disarray after Mr. Sadat's assassination. Mr. Mubarak told Al Ahram's chief editor, Ibrahim Nafeh, that most of the plotters had been rounded up in recent sweeps and that their encampments and hideouts were ''falling one hour after another.'' This was seen as an indication that the Government's search for suspects was still under way. Al Ahram, in an article today on the interview, quoted Mr. Mubarak as asserting that the ''fanatic'' plotters intended to annihilate the nation's political, military and religious leaders to erode the underpinnings of Mr. Sadat's Government.