In California, the watch for the royal yacht Britannia is about to begin. And members of the committee that will host Queen Elizabeth II at her first big Hollywood outing all have one thing in common: big money, representing a big bank, a big store, a big aerospace business, a big studio, big oil and big Reagan supporters.

Eight California moguls are picking up the dinner check at 20th Century-Fox the night of Feb. 27 as a big, friendly gesture to the American taxpayer. "We're doing it because we want it to be a private enterprise situation," says John M. Heidt, bandleader Horace Heidt's son and president of Union Bank, owned by Standard Chartered Ltd. of London. "We feel comfortable about it."

Stockholders should feel comfortable about it, too. Heidt says expenditures for the event are "not open-ended--as businessmen, our obligation is to our stockholders."

Serving with him on the Los Angeles Host Committee, in whose name the White House sent out dinner invitations last month, are Rockwell's Robert Anderson, Atlantic Richfield's Robert O. Anderson, 20th Century-Fox's Marvin Davis, Union Oil's Fred L. Hartley, Bullock's Bruce M. Schwaegler and Reagan "kitchen cabinet officers" Justin Dart and Holmes Tuttle. All are there at the invitation of Tuttle, who has had some prior success rounding up big money. "I accepted with great pleasure," says Heidt.

Tuttle, a retired Los Angeles automobile dealer, performed a similar service for the Reagans two years ago by passing the hat among Midwestern oil men. Much to the amazement of some in the White House--and the embarrassment of others who subsequently ordered him to stop--Tuttle wound up raising $800,000, tax-deductible, for the controversial White House renovation fund.

The Fox dinner on Stage Nine, where until recently "M*A*S*H" was filmed, no longer is the intimate get-together of real and celluloid royalty that it started out to be. The guest list has escalated to nearly 500 names. Only a few will be introduced to the queen--among them Los Angeles Mayor Tom Bradley and freshman Sen. Pete Wilson--despite lobbying in high places for a full-blown receiving line. There's been so much lobbying, in fact, that at times the board rooms of California have resounded like the cloakrooms in the U.S. Capitol.

Of all the invitations connected with the queen's Feb. 26-March 4 California visit, the ones with the most status are for dinner aboard the Britannia. There will be opportunities in San Diego, Los Angeles, Santa Barbara and San Francisco, and one constant at them all will be the president's personal representative, Deputy White House Chief of Staff Michael K. Deaver, escorting Her Majesty. While three of the dinners have full tables of 56, the one in Santa Barbara has a smaller guest list. Some Reagan cronies who live nearby had been hoping that the queen would set extra places for them at her royal board. So far, they've gotten nowhere.

In San Francisco, the Reagans will get an assist from four other corporations in the dinner they are hosting for the queen and Prince Philip March 3. While it's Frank Sinatra, Perry Como, Ed McMahon, Dionne Warwick and George Burns entertaining Her Majesty in Los Angeles, in San Francisco it will be somewhat more high-brow with a performance for 250 guests by the San Francisco Opera Company and the San Francisco Symphony.

Bank of America, Crocker Bank, Wells Fargo Bank and Standard Oil of California are underwriting production costs, and the State Department, as usual, is paying for the food.