LONDON (AP) _ Thousands of shoppers made a mad dash for bargains on fine china and cashmere when Harrods department store simultaneously opened its 11 doors today for the first day of its annual January sale.

''People have to get here and get it before anybody else has got it,'' said Clive De Boer, a store director.

Twenty security guards at the main entrance controlled the streams of bargain hunters, many of whom had clustered outside in the early morning hours waiting for the store to open.

Three young men wore animal costumes, apparently hoping to win the attention of about 60 reporters and photographers covering the beginning of the sale.

Harrods expects to surpass its sales record of last year, said Robert Hampson, a merchandising director. ''Trade has been very strong generally, so we feel it will be good today,'' he said.

Fewer Americans probably will show up this year because Harrods didn't advertise in the United States, as it did in 1986.

However, Hampson said: ''The feeling from the store is that there has been a resurgence in tourism after the last few months of doldrums.''

Harrods took in $8.82 million on the first day of its sale last January, a single-day record. It took in $56.7 million altogether in that sale. The sale lasts all month.

Other London stores began their January sales right after Christmas. Unlike U.S. retailers, which hold sales throughout the year, big British stores mark down their merchandise only twice, in January and in the summer.

Harrods said it expected 200,000 shoppers on the first day this year.

It hired 2,000 extra workers to help the 4,000 it regularly employs and beefed up its security staff to 100.

''You can get rowdiness and aggressiveness among customers who get angry among themselves,'' said Peter Jones, manager of the uniformed guards.

And when the pubs close from 3 p.m. to 5:30 p.m., Jones said, ''You get a little drunkenness.''

But shopping was the order of the day.

''Luxury items at markdown prices always draw very well,'' Hampson said, noting the china and cashmere departments are very popular.

Twenty-seven seconds is the record time for the first customer to reach the china sale, Harrods said.

In that sale room, shoppers caused a great clink-and-clatter as they filled baskets with their choices. Salepeople were expecting some breakage, one of them said.

Elaine Stulberg of Los Angeles, who had traveled to Rome with her son Barry, said of the sale: ''We decided to come here for the sale. We decided to make an extended trip of it. We just wanted to see what it was all about.''

But Mrs. Stulberg, who headed straight for the cashmeres, was a little disappointed.

''I'm looking already and seeing that the prices aren't bargains after all,'' she said.