A new, relatively cheaper era in transatlantic air services dawned yesterday as the Civil Aeronautics Board permitted "standby" round-trip fares of $256 to take effect for travel between New York and London.

In addition, the regulatory agency yesterday authorized the start this morning of new "budget" fares for the Atlantic crossing, at a higher rate than those proposed and rejected last week.

But the CAB turned down for the second time an appeal by Pan American World Airways for a waiver from last week's budget-fare decision. The international carrier already had sold some 1,600 tickets for flights starting yesterday at prices the agency turned down.

Pan Am officials were busy last night attempting to contact 230 consumers who had purchased tickets for flights today at advertised fares of $256 for a round trip. These customers now will have to pay $280 for a round trip -- the budget-far level approved yesterday for inauguration today.

Although Pan Am's customers must pay more, the CAB decision to permit airlines to offer budget fares as of today eased what could have been a painful confrontation between Pan Am and its customers if they had to come up with the normal far of $625 between Britain and New York.

Ironically, as the low-far flights began yesterday, the company that brought about the new era -- Laker Airwasy, Ltd., of Britain -- still was getting r eady to begin its first transatlantic flights on Sept. 26.

Laker began a struggle to win government authority for cut-rate North Atlantic air travel more than six years ago. President Carter gave final U.S. approval for Laker last June, one week after the CAB recommended a one-year experiment in lower fares.

Other airlines, which had fought bitterly to block Laker's no-frills concept, immediately jumped on line at the CAB with proposals of their own for discount rates.

After a series of complicated decision here and abroad, the following new fares were being offered for travel between New York and London as of yesterday:

"Standby" fares of $256 will be available for round trips, provided customers are willing to line up for available seats. The seats on that day's flights will be assigned starting at 4 a.m. on the day of the flight. Companies planning to offer such fares are Trans World Airlines, Pan Am, British Airways, Iran Air, Air India and El Al.

TWA said yesterday it will start the $256 round-trip fare (eastbound oneway fare will be $146; westbound, $110) next Tuesday from New York to London. Standby fares from London to New York started yesterday.

Pan Am also began corrying standbys yesterday. A spokesman said about 50 persons showed up in New York at Kennedy airport and the airline was able to find seats to London for 24.

Airlines are setting aside separate waiting room sections for standbys, and tickets must be purchased at least three hours before departure. Customers who get standby seats will receive noraml economy service, including meals.

British Airways said it will begin a $255 round-trip standby fare starting next Monday. The British company had proposed a "super Apex" (advance purchase excursion) fare of $299, which the CAB turned down.

A "budget" fare of $280 takes effect today, earlier than the Sept. 26 date originally approved by the CAB and higher than the $256 rate proposed by airlines. Passengers must buy tickets at least 21 days in advance of the week planned for departure, and the air firm assigns the day of departure in that week one week before takeoff.

The new plan includes a penalty of $65 for failure to show up, a Pan Am spokesman said. Airlines last night were filing final tariffs for the so-called "budget" fares. Acting upon earlier CAB advice, TWA had told customers the budget fares wouldn't be able to start until Sept. 26.

Laker, meantime, will begin service later this month with fares of $236 for a round trip. Passengers will gain seats on Laker flights on a first-come, first-served basis, with assignments beginning six hours before departure.