More than 2,000 U.S.-bound air travelers - many of them American families returning from European vacations - have been forced to camp out on London sidewalks while waiting to buy low-cost standby tickets.

Nearly another 2000 are doing the same at London's Heathrow and Catwick airports.

Some have been there for as long as five days. More are coming all the time. For many there is no hope of a flight for at least a week. All are discovering they have few alternatives but to wait.

Lured to Europe by the new cheap U.S.-to-London air fares, thousands of thrifty fliers have been arriving weekly since spring. Now, however, as they turn their faces homeward, they are finding themselves engulfed in the peak summer season when few seats are available at any price.

Those standby tickets that are available can be had only by holding down places in long lines that take several days to reach the ticket window.

British authorities are viewing the situation with alarm. Late Wednesday night the British Airports Authority announced that it would seek an injunction that would ban the six transatlantic carriers from selling standby tickets at Heathrow, which the authority operates.

Heathrow is often crowded to capacity in normal circumstances, but for the past week as the standby influx has increased, the airport has found itself all but unable to operate with the standby seekers literally under its feet.

Pan American and British Airways have moved most of their standby sales operation from Heathrow to their downtown London terminals. TWA, however, has continued to sell at the airport despite pleas from the authority. TWA contends that it is up to the authority to provide facilities for standbys as they would for passengers paying any other fare.

The authority's injunction will be heard in the high court as soon as a judge is available. That may be three or four days, as there is a line for judges as well. TWA condemned the injunction bid and has vowed to fight it.

Meanwhile more and more hopeful standbys are pouring into London from all parts of Europe.

Outside the Victoria Station offices of the Laker Skytrain, which pioneered transatlantic standby travel last September, an estimated 1,500 ticket seekers sat in a line along the sidewalk. Their backpacks and sleeping bags made a crazy-quilt of brilliant colors along the pavement. Some read: some slept; some meditated. No one new for sure when they would get a flight.

A Laker official at the scene said: "It will be Sunday before we have all these people out of here. But by then, there's bound to be twice as many others."

Another 1,500 were waiting in similar lines at Skytrain's base at Gatwick airport, south of London. The situation there was eased somewhat as a special section of the terminal complex has been set aside for standbys.

At Pan American's downtown London terminal, some 300 hopefuls waited over Wednesday night and another 100 joined them yesterday. During the day, Pan Am has been making its building available to the standbys. But at 4 p.m. the building closes and the standbys are forced to take refuge in an unused tunnel behind the terminal. There they have tried to sleep on mats made from cardboard. They wrap themselves in anything they can find that will protect them from the cool, damp British summer weather. Lucky ones have their own sleeping bags, but most do not. No toilet facilities are available during the night.

The Pan Am standbys have organized a list so that those who line up do not have to stay personally in line, thus allowing them to seek a few hours respite in nearby parks. However, roll calls are held three times a day, and anyone not present has his order name struck from the list.

No one knows who started the list. It has been handed down from group to group for several days.

At the Lake Victoria ticket window, however, trouble broke out Wednesday night when line-jumpers attempted to break in at the head of the line. A scuffle ensued and the interlopers tried to seize a list being kept there as well. Police intervened and broke up the fight, but they also confiscated the list in an attempt to prevent a future fracas.

The airlines, as part of their standby sales policies, are not allowed to keep such lists, but they do not discourage passengers from organizing their own.

Many of the travelers are young Americans who have been hitchhiking around Europe for several weeks and who have come to London with only enough money to pay for their air ticket home. Not expecting a four or five-day delay here, they have run out of money. Some have sought emergency loans from the U.S. consulate. Others have taken to panhandling in order to have enough funds to eat.

Not all of the passengers are young. Betty Lawson, a dietician from College Park, waited fruitlessly with her three children for two days at British Airways before joining the Laker queue.

"We might make it the day after tomorrow," she said with more hope than faith. "It is hard to tell how many people are here, really." She gestured to the ragged line of bodies stretched out in various positions along the sidewalk. For Lawson and other families, buying a full-fare ticket home is prohibitively expensive. The standby fare from London to Washington is $140, whereas the regular economy class fare is $428.

Wayne Partenheimer, a young attorney from Trenton, N.J., starts a new job on Monday.

"I just have to be there," he said, shaking his head as he looked over the Pan Am line. "They say there may be some seats tomorrow to Seattle. Looks like I'll have to go there and then fly back to Philly. But even at that," he added with half a grin, "it will be cheaper than paying full fare directly from London."

The situation is going to get worse before it gets better, airport authorities say. They fear that many people traveling on the continent or even in Britain are out of touch with the news and will not be aware of the standby bottleneck until they arrive here.

As the mellow twilight of a rare sunny evening settled over London last night, the Pan Am standbys filed into the park across the street from the terminal. It was time for the roll call.

"Majorica."

"Here."

"Wong."

"Here."

"Abrahams."

The names and replies were as ordered and as stark as the standby advisory board at the British Airways Terminal around the corner.

New York. Full.

Miami. Full.

Washington. Full.