The buildup of the big British naval task force sailing to the South Atlantic in the Falkland Islands crisis continued today, as the rest of Britain began the traditional long Easter weekend waiting for what may happen Monday, when the first hostilities have been threatened.

Diplomatic sources here said it was uncertain how much could be accomplished before then by U.S. Secretary of State Alexander M. Haig Jr.'s mission to mediate a peaceful Argentine withdrawal from the Falklands in return for a compromise by Britain on Argentina's sovereignty claim.

Haig's five hours of talks with British Prime Minister Margaret Thatcher last night left alive a number of possibilities for a diplomatic solution as he flew today from here to Buenos Aires, the sources said. But they were unwilling to express either optimism or pessimism about the prospects of avoiding war between Britain and Argentina.

They suggested that Britain still would be willing to settle for some form of British administration rather than continuing sovereignty over the Falklands, provided that Argentina withdraw its forces first and that a sovereignty settlement were acceptable to the 1,800 residents of the islands. The sources said this should leave Haig room for maneuver in his talks with the military government of Argentine President Leopoldo Galtieri.

Haig, while en route to Buenos Aires, conferred by telephone with President Reagan, who was at the Barbados residence of actress Claudette Colbert, Washington Post staff writer Lou Cannon reported. The call, placed at 5:45 p.m. Barbados time, lasted for five minutes.

An announcement by the White House press office said that the president, who is vacationing in Barbados through Sunday, will continue to receive written reports from Haig's party during the day on Saturday.

Reagan is scheduled to make a five-minute radio address to the American people on Saturday, but aides said late Friday that his remarks will focus on aid for Caribbean nations rather than on the situation in the Falklands.

Meanwhile, the requisitioned British luxury liner Canberra, with about 2,000 Marine commandos and Army paratroopers and their equipment aboard, sailed this evening from Southampton. Since it docked there Wednesday after a world cruise with 1,600 passengers, the 45,000-ton P&O Line ship has been refitted rapidly and provisioned for military transport duty.

The Canberra and a cargo ship that left last night loaded with tanks and other military equipment will be joining 27 British warships already at sea. According to the government, most of them are still a week or two away from the Falklands. They include two aircraft carriers, one assault ship, two light cruisers, five destroyers, five frigates, five landing ships, four fleet oil tankers and three supply ships.

Absent from the government's official list are several nuclear-powered hunter-killer submarines believed to have arrived in the South Atlantic. Other warships also are being prepared for relief duty with the task force, and more civilian vessels, including oil tankers, have been requisitioned.

Analysts expect the task force to be used primarily for a blockade of the Falklands and possibly the ports of Argentina, which seized the islands off its southeast coast last week. They do not expect, at least initially, any British attempt to land troops on the Falklands, where Argentina has built up and fortified an occupation force of about 8,000 troops, compared with the few thousand being transported by the British task force.

A blockade by surface ships would make refueling a serious problem thousands of miles from the nearest British base, according to military analysts.

Britain appears to be depending, at least initially, on the ship-sinking threat of its nuclear-powered submarines, which do not have to surface or refuel. They are believed to be the weapon with which Britain has threatened to attack any Argentine warship or civilian ship being used for military supply purposes within a 200-mile-radius around the Falklands beginning Monday. Responding to this increased British pressure for an Argentine withdrawal from the Falklands, Galtieri said an attack on an Argentine ship would meet an armed response.

The outcome of Haig's talks in Buenos Aires will be watched closely by Thatcher, who went today to the prime minister's country residence at Chequers. Whether she remains there or meets with senior Cabinet members there "will depend on events," an official said. "Nobody envisions any particular developments for a few days."

Otherwise, outside of the defense and foreign ministries, most of the government will be shut down as usual from today until Tuesday. Banks, businesses and most stores also are closed, and no newspapers are published on Good Friday and Easter Monday here. Parliament is in recess until April 19 unless Thatcher summons an emergency session.

Last night, Foreign Secretary Francis Pym broadcast a special message on the British Broadcasting Corp. World Service to the 1,800 Falkland Islanders, whose safety would be at risk in a British-Argentine battle for the islands. Pym said Britain was doing everything it could to restore their position to normal as soon as possible.

"By that I mean, of course, bring about by peaceful means, if we can, the withdrawal of the Argentine forces who have absolutely no right to be there," Pym said.

In an Easter message on the same "Calling the Falklands" service, which has been increased by the BBC from once to three times a week during the crisis, the archbishop of Canterbury, Robert Runcie, asked the islanders to pray that anger and national pride would not cloud wise judgment in the search for a peaceful settlement.

"The prayers of all our people are with you in these days of crisis and uncertainty," he told the islanders, who are believed to be still receiving the broadcasts. "You may be far away, but your interests, your safety and your well-being are at the very heart of our thoughts this Eastertide."

Meanwhile, 15 civil servants in the Falkland Islands community sent a letter to the Foreign Office appealing to Britain to evacuate the population before any fighting begins. The letter was sent out to Uruguay.

The Foreign Office said Friday night that the International Red Cross had been asked to take "an interest" in the fate of the islands' 1,800 residents, Reuter reported.