With fists full of cashmere sweaters, bags full of Scottish salmon and wallets full of dollars, Americans in apparently unprecedented numbers took advantage of Britain's crumbling currency today and headed for the cashier counters at Harrods as this city's most famous and fashionable department store began its annual New Year's sale.

An estimated 300,000 people will pass through the store in the first two days of the three-week sale. And while the opening-day throng was overwhelmingly British, the twangs of New York, Dallas, Charleston and Los Angeles -- not to mention Tokyo -- were unmistakable wherever the groping for goodies was most serious.

"It's a great sale. We got cashmere sweaters, real good brands, that go for $225 to $250 in the States that cost 64 pounds the equivalent of $73 here," said Ettaleah Bluestein of Charleston, S.C. "And the service people at the store are the nicest I've seen anywhere, even nicer than in the South," she added, shepherding her husband and three children to the next counter.

Jeffrey Ressler, a New York attorney, said he paid 160 pounds ($184) for a Burberry raincoat elsewhere in London "that would cost $400 to $500 in New York, and I get the tax back at the airport. So you can fly here and buy a raincoat for the price of the coat in New York."

That, in fact, is what Harrods is hoping a lot of Americans are doing. The store advertised for the first time last month in The New York Times, hoping to make a virtue, and some money, out of Britain's plunging pound.

"We've got cashmere sweaters to take home in this bag, and lox to eat in the hotel in that bag," said another New Yorker with a big smile. He declined to give his name because he didn't want his friends to know he brought food back to the hotel. "Do they sell bagels here, too?" he asked.

The Harrods sale has become a tradition. Crowds flock each year to this store whose sale prices can frequently be beaten elsewhere in the city, but whose glamour, glitter and distinctive gold and green shopping bags seem to mean a bit of the good life to a lot of people who ordinarily don't shop there.

This year, however, there is a difference -- the booming dollar and the sinking pound sterling. Now valued at $1.15, Britain's once-proud currency is worth half of what it was in 1980. The pound is now worth 25 percent less than it was last January.

The combination of sale prices and the good exchange rate has meant that 25 percent of the store's business this past year has been with American tourists, store officials said.

Last January Harrods took in some 28 million pounds in the three weeks of the sale, and this year Alexander Craddock, chairman of Harrods, estimates the take will exceed 30 million pounds. The only estimate on the number of Americans who will pass through the store, however, is determined by the number who actually turn in applications at the airport to get their 13 percent value-added-tax refund, according to store officials.

Interviews with Americans shopping here today produced uniform praise for the civility of sales clerks handling the stampede of tens of thousands of shoppers through the store's 11 doors.

"It's not the madhouse I expected," said Jim Gallaher of North Carolina. "Everyone's real helpful and very well mannered." Vivien Rassler said, "The service is excellent. If this were a New York sale, the rudeness would overwhelm you." Lillian Turner, a New York-based TWA employe, said she took a flight here just for the sale. Although Harrods is as busy as jammed New York stores, "You don't mind the crowds here."

A few bargain-hunting Britons camped outside the store last night, and by opening time some 3,000 were lined up outside, streets were blocked off and huge traffic jams had developed around the Knightsbridge neighborhood.

Another difference this year is that so far no terrorist bombs have gone off. On Dec. 17, 1983, a bomb planted at the store by the Irish Republican Army killed six persons and injured 91 others. This year no parking was allowed in front of the store, to avoid car bomb attacks. Police were very much in evidence outside, and before the doors opened sniffer dogs were led through all six floors of the famous structure.

In fact, this year everything seems relaxed and pleasant. British actress Lorraine Chase, one of the early shoppers, tried on a Russian golden sable coat marked down from 60,000 pounds to 30,000 (about $34,500). "This is the price of a house that I've got on my back," she said, putting the coat back. Two $3,500 mink coats were snapped up in a few minutes, their prices cut in half.

At a crowded chinaware counter, however, Harrods looked for a moment, at least, like any other store. "I thought I told you to stay put, 'enry," an irate British woman said to her husband, Henry, who had apparently wandered off into the mass of humanity under the weight of several green-and-gold bags. But she admonished him in hushed tones.