Millions of Americans died or were seriously injured last year in domestic accidents ranging from car crashes to choking on their dinner, Britain's newly designated ambassador to Washington, Antony Acland, told the American Chamber of Commerce here last week. Since only a relative handful were killed or injured in terrorist incidents overseas, Acland said, Americans should realize that "it is, in fact, far safer to travel abroad than to stay at home."

Acland's comments were part of a campaign that has enlisted virtually every government official who has found himself in front of a U.S. audience in the past several weeks. In an interview Friday with U.S. television networks, Prime Minister Margaret Thatcher noted that "the chance of being affected by terrorism in this country is about the same as the chance of being struck by lightning."

"Please come," Thatcher implored in the interviews. "We miss you."

The public statements coincide with new promotional offers to lure Americans across the Atlantic, including free airline tickets to London and special teas at Harrods department store, and a nationwide U.S. advertising promise that "We Speak Your Language."

Whether American travelers can be persuaded is a crucial question for the tourist industry throughout Europe this summer. So far, airline, tour and hotel cancellations in Western Europe are running from 10 to 70 percent.

Concern about terrorism tops the list of reasons for bypassing Europe, according to industry spokesmen. But close behind has come new anxiety about radiation fallout from the Soviet nuclear accident in Chernobyl. Many of those brave enough to make the trip have been put off by the current weakness of the U.S. dollar against European currencies.

In Britain, which sees itself as a safe and orderly society, a special friend to Americans and a deserving ally for its support of the U.S. raid against Libya, the cancellations are considered an insult as well as an economic injury.

The dismay they have provoked has been compounded by earlier predictions that 1986 would be the biggest year ever for the British tourist industry, building on record-breaking 1985. The 3.3 million U.S. tourists who traveled here last year, spending nearly $2 billion, were more than the total visiting all of the rest of Europe.

Early indications that trouble was ahead followed terrorist attacks at the Rome and Vienna airports on Dec. 27. Then came the April 2 bombing of a TWA jet en route from Rome to Athens, and the bombing of a West Berlin discotheque April 5.

But not until April 15 dawned with the news that U.S. jets had taken off from British bases to bomb Libya were the implications of the rash of terrorist attacks brought home here. No sooner had Libyan leader Muammar Qaddafi threatened retaliation against Britain, as well as the United States, than a bomb was discovered being carried aboard an airliner at London's Heathrow airport. Although the incident apparently was unrelated to the Libyan incident, its timing could not have been worse.

Less than a week later, a central London office shared by British Airways, American Express and American Airlines was bombed.

By the end of April, as thousands of vacations were canceled, it was clear to the British tourist industry that 1986 was not likely to be a boom year.

Although many hotels and tourism organizations here are reluctant to give figures, representatives of some travel agencies estimated that bookings for central London hotels are down by about 40 percent. The British Incoming Tour Operators Association has estimated that the number of American tourists this month has dropped by 25 to 30 percent.

In the London theater district, where three major new musicals this summer hoped to follow the sell-out trends set by Andrew Lloyd Webber's "Cats" and "Starlight Express," there are fears of imminent disaster. In normal times, foreign visitors make up 45 percent of theater audiences here, with a third of those from the United States. Highly dependent on blocs of seats sold to tour groups, some of the shows now expect to be playing to half-empty houses.

British Caledonian Airlines, which has the misfortune of deriving a large portion of its income from transatlantic flights and what until recently were twice-weekly round trips to Libya, announced this month that it was laying off 1,000 employes. British Airways, which says its business has fallen by only 10 to 15 percent and is now beginning to spring back, nonetheless has canceled the planned recruitment of 1,500 extra summer staff.

To many Britons, American fears seem irrational and a bit unseemly for a nation that calls itself the "home of the brave." An initial response was a series of tongue-in-cheek media interviews with "heroic" American visitors. One hotel in Torquay, in southwestern England, awarded a U.S. couple staying there a special certificate and a newly invented "Purple Heart Cocktail."

One local tourist agent marveled at a vacationing American couple "who were so scared to fly from New York to London that they actually booked a flight from New York to Dublin, and then flew here, thinking it was safer." Many Londoners consider Dublin a haven for Irish republican terrorists, and believe flights to and from its airport to be among the most risky they can make.

There is substantial resentment here also of what British Airways Chairman Lord King last week implied were sensationalized views "being given to the American people by the American media about the hazards of traveling to the United Kingdom and Europe on business or pleasure."

Extensive media coverage of terrorism, Acland told the Chamber of Commerce, "has created quite unjustified anxiety about overseas travel . . . . Britain is still a very safe place to live in and to visit, and British airlines and British airports have a safety record which is, quite simply, second to none."

Among widespread efforts to stem the anxiety, the British Tourist Authority is organizing a tour of key American cities by what have been described as leading British celebrities and well-known Americans living here.

This weekend, Harrods will join various government and industry organizations in sponsoring a three-day tour of London for American travel agents. In addition to a shopping spree and tea at the department store, agents will be given pep talks by the deputy commissioner of the London police, a commercial attache from the U.S. Embassy and tourism industry officials.

British Airways is offering 5,600 free round-trip tickets, to be chosen by lottery, on its June 10 transatlantic flights from 15 U.S. cities. And, if all else fails, there are widespread hopes that the July 23 royal wedding between Prince Andrew and Sarah Ferguson will prove an irresistible draw to thousands of heretofore queasy Americans.