Allegis Corp., which owns United Airlines, began shedding its other assets yesterday with the announcement that it is selling Hilton International Co. to Ladbroke Group PLC, a British leisure and hotels conglomerate, for $1.07 billion.

The deal was the first in a series of anticipated divestitures for Allegis, which once aspired to be a travel conglomerate. In June, less than three months after Allegis acquired the Hilton International chain of hotels, its board declared that it had lost faith in the diversification strategy and accepted the resignation of the strategy's architect, former Allegis chairman Richard J. Ferris.

Ladbroke beat out approximately 20 other bidders for the hotel chain, including Bethesda-based Marriot Corp. and Lufthansa, the West German airline. Ladbroke's bid is about $90 million more than the $980 million Allegis paid for the hotel chain on March 31, a price that critics said at the time was too high.

The package includes 91 hotels worldwide, including the Vista International Hotel in Washington. Most of the hotels are in Europe.

Ladbroke will also acquire a 20-year management agreement for Hilton to operate the 600-room Toronto Westin Hotel, along with an option to renew the agreement for another 30 years. The Toronto hotel is owned by Westin Hotel Co., another Allegis subsidiary that is on the block.

Hertz Corp., still another Allegis unit, is expected to be sold next.

Analysts said the price received for the Hilton hotel chain appeared to be in line with earlier estimates of its value. "It's the first positive sign. It's been all talk so far," said Paul P. Karos, an industry analyst with L.F. Rothschild.

Frank A. Olson, who took over Allegis' chairmanship on an emergency basis in June, said the transaction -- which is subject to approval by the shareholders of Ladbroke Group and certain regulatory clearance -- "brings us a step closer to fulfilling our commitment to enhance shareholder value through a restructuring of Allegis Corp."

The proceeds from the sale will be used for dividend payments to shareholders, but those payments will not occur until early 1988, said Allegis spokesman Matt Gonring.

Ladbroke said it will finance the acquisition with bank loans and by issuing additional shares.

While the announced strategy of the Allegis board is to sell off assets and pare its business back to running one of the nation's largest airlines, several questions surround the corporation's future.

One question is who will lead the company. A search committee has been formed to find a permanent replacement for Ferris. Olson, who headed Hertz until he stepped into the vacancy left by Ferris, might get the job permanently. Flying Tigers Chairman and chief executive Stephen M. Wolf has also been mentioned as a possible candidate.

United's pilots, who opposed Ferris' notions of turning the airline into part of an integrated travel services corporation and put the company into play last spring with an offer to acquire the airline, are continuing to pursue ownership. William R. Howard, chairman and chief executive officer of Piedmont Aviation, has been hired to head the pilots' Airline Acquisition Corp.