Waves of Israeli warplanes today bombed Palestinian guerrilla positions in Beirut in retaliation for the shooting yesterday of Israel's ambassador to Britain.

The raids killed at least 45 people, according to Lebanese reports, and caused heavy damage. Guerrillas responded by shelling Israeli settlements in northern Galilee.

Israeli jets also bombed Palestinian positions in southern Lebanon, and a cross-border artillery duel continued after dark, leaving one Israeli civilian dead and three wounded in communities near the border.

The new violence represented the most serious breakdown yet of the 10-month-old border cease-fire between Israel and the Palestinians. It was the heaviest Israeli raid on Beirut since July 17, 1981, a week before the cease-fire, when about 300 Lebanese and Palestinians were killed.

Prime Minister Menachem Begin's press secretary, Uri Porat, said tonight that "Israel's action today ended a long period in which Israel showed restraint, and with this murderous attack Israel could not but act in the way it did."

Amid increasing military pressure on Begin to give the go-ahead for a full-scale invasion against Palestinian bases throughout Lebanon, Israeli officials said there is evidence of a coordinated "new wave of Arab terrorist activity" against Israeli missions in Europe. They said the terrorist actions start in Lebanon.

Following the shooting in London of Ambassador Shlomo Argov, the most senior Israeli diplomat yet to be the target of an assassination attempt, Foreign Minister Yitzhak Shamir condemned what he called "the despicable attack by Arab terrorists," and said the ministry was waiting "with deep anxiety" for the outcome of attempts to save the life of Argov, who underwent brain surgery.

Hours later, the Israeli military command announced that it had been ordered to send the Air Force against the Beirut targets "as a result of the criminal attack and other breaches of the agreement on ceasing hostile activities."

The military said Israeli jets bombed a combat training installation of Fatah, the main faction of the PLO, and an ammunition depot and weapons storehouse beneath the grandstand of a Beirut soccer stadium. An army spokesman said "hundreds of meters" of weapons caches, including mortars and other weapons, had been stored there.

Apparently anticipating retaliatory shelling from Palestinian artillery positions, Israel also bombed rocket launcher sites and 130 mm gun emplacements in the Nabatiyeh region of southern Lebanon, military officials said.

Shortly after the three-hour Israeli air raid on Beirut, Palestinian gunners in southern Lebanon opened fire on Israeli border settlements in the western Galilee region and the Galilee panhandle that juts northward to the Israeli border town of Metulla. One Israeli civilian was killed in the car he was driving and three others were wounded during the shelling, although military authorities would not disclose where the casualties occurred, so as to prevent the Palestinian gunners from pinpointing their artillery range.

Israeli artillery units near the frontier opened fire on the guerrilla gun emplacements in the worst cross-border exchange since Israel and the PLO agreed to the cease-fire arranged last July by U.S. special envoy Philip C. Habib.

The Israeli military command did not say how many planes were involved in today's raids but it said all returned safely.

It was the first crossborder exchange since May 9, when Israeli jets bombed and strafed guerrilla positions along the Lebanese coast and Palestinian gunners retaliated by shelling northern Galilee, reportedly causing no casualties or damage.

Israeli Foreign Ministry officials described Argov as "one of the most brilliant diplomats we have in the foreign service."

The Foreign Ministry said, "We are confident that the British authorities will conduct an energetic investigation and will take all the necessary steps to ensure that all those involved in the assassination attempt will be punished and that any such future attempts will be prevented."

Following a disclaimer of responsibility by the PLO office in london, Avi Pazner, spokesman for the Israeli Foreign Ministry, said, "It is beyond doubt that those who executed this hideous act are Arab terrorists. There is no credibility to any denial by the PLO."

He said, "There is no doubt we are in a presence of a new wave of terrorism against Israeli targets in Europe. There is a repetition of murderous acts against Israeli diplomats. It appears the terrorists feel that in Europe they are more at liberty to conduct such actions against us."

On April 3, Yacov Barsimantov, 43, a second secretary in the Israeli embassy in Paris, was shot to death. Israeli officials said there was "definite" evidence linking the PLO to the woman who shot Barsimantov and then escaped.

At Barsimantov's funeral, Shamir angrily said, "I can promise you, we will use all the force at our command to crush the terrorist organizations everywhere our hands can find them. We will strike them without mercy, because we have decided to live."

Several days before the Barsimantov slaying, three men opened fire on a Paris building housing an Israeli purchasing mission, but there were no casualties.