The Civil Aeronautics Board moved quickly yesterday to award other airlines temporary authority to take over Braniff International's three major foreign routes that weren't leased already by the shutdown carrier to Eastern Airlines.

The CAB late yesterday awarded Braniff's route to London from Dallas/Fort Worth to American Airlines, Braniff's arch competitor after Braniff filed under Chapter XI of the Bankruptcy Act. Continental Airlines was given Braniff's route to the cities of Maracaibo and Caracas in Venezuela, and Eastern Airlines was told it could add Dallas-Mexico City to its route network.

The awards were made quickly in an attempt to preserve U.S. airline service on the routes. The board made its decisions within hours of accepting applications from the carriers. Nine airlines wanted the London route, eight wanted the Venezuela route and only Eastern wanted Braniff's Mexico City flights.

The board said the route authority was good until April 26, 1983, and that it will decide between now and then which carriers will get Braniff's permanent authority to operate the routes. It emphasized that the airlines getting the temporary authority didn't have an "inside track" for permanent authority.

Thomas G. Plaskett, American's vice president for marketing, said the airline will begin its new London route--its first to Europe--next Wednesday with a Boeing 747 and will honor all Braniff's Dallas-London tickets held by passengers.

Eastern, which takes over most of Braniff's South American routes under an arrangement approved by the CAB last month, was forced to cancel its first Braniff replacement flight scheduled for Thursday to Panama because of a paperwork problem in Panama. But Eastern officials expressed confidence yesterday that its resumption of Braniff's services would go smoothly and that all flights would be in place before June 1, its original startup date.

Airlines scrambled yesterday for landing rights from the Federal Aviation Administration to begin service on Braniff's domestic routes. United Airlines, an early winner, yesterday morning began flights to Dallas from Chicago and Denver, two key cities on its route network.

Washington-based USAir said it has been given slots--as landing rights are called--to begin service next week between Dallas and New York LaGuardia Airport.

Meanwhile, Braniff officials in Dallas began drawing up an inventory of the airline's assets and collecting information on outstanding claims, said a tired Sam Coats, Braniff's senior vice president for marketing. Coats is one of 225 Braniff employes still on the payroll. Besides closing down, he and the others will be seeking to reorganize the airline into a smaller entity under the supervision of the bankruptcy court, he noted.