At Claridge's the posh Mayfair hotel that caters to kings, queens and Henry Kissinger, there is a surefire recipe for success in the kitchen.

Sprinkle garlic, pepper and salt over the ratatouille, bind the hamburger meat with egg and don't mix union activity with the Caesar salad.

Richard Elvidge, a 19-year-old apprentice chef, failed to master these rules and so he was sacked last month. His plea for reinstatement is making culinary, cultural and industrial history here.

Elvidge insists he was fired only because he tried to recruit the Down-stairs at Claridge's into the General and Municipal Workers' Union.

"I worked there for 19 months and didn't have any complaint until I started up the union," he says. "They got rid of me because I'm a shop steward."

Stuff and nonsense, snorts Sir Hugh Wontner, who works Upstairs in a penthouse suite and is chairman of the Savoy Group, owner of Claridge's and other smart hotels around town. We never knew Elvidge was a union man until we read it in the papers, Sir Hugh wrote to the Times of London, a sort of bulletin board for Top People.

ELVIDGE WAS CANNED, Claridge's insists, because in his two years at Grimsby Technical College he never learned to emulsify the mayonnaise, cut the vegetables evenly, trim the tails from herring hors D'ouvres, reason that ratatouille or perform the other rites required to feed the very rich.

This slice of social anthropology is being retailed daily before a government-created industrial tribunal. There, Elvidge must defend his egg-less hamburger and Claridge's must explain why his union chores never inflenced the hotel's decision.

Before Elvidge went to the tribunal, and on the first day of the short-lived strike his dismissal touched off, the hotel's assistant general manager, Michael Bentley, explained why unions and Claridge's go as poorly as claret with fish.

"Claridge's is to some extent an old fashioned hotel," he said. "I mean it's a very personal hotel. The relationship that the staff has with the client is a very personal one."

Claridge's is a 163-year-old hostelry, currently clad in the red brick of the Dutch revival that was the rage here 80 years ago. Inside, it is all intersecting planes and sparatan reliefs that passed for modernity in the 1920s.

The place caters smoothly to the rich and famous. It barely turned a hair when Kissinger showed up with his entourage, demanding 20 rooms, or President Carter, mindful of his populist image, pulled his staff out from a floor on two days' notice.

Ordinary mortals with $100 to pay for the night can get double at Claridge's - provided they book well in advance.

WHEN ELVIDGE was fired on April 7, about 120 of his 570 fellow workers walked out in protest. They "came chiefly from the youngest element in the kitchen, occupying the lesser positions, and from the hotel floors . . . a majority of the young maids, some on permit from abroad," said Sir Hugh.

The strikers were young. They are largely excluded from the pool of tips and get little more than the minimum, $65 a week. Tips at Claridge's matter. The gold-braided doorman, who walks clients' poodles and summons taxis, picks up nearly $300 a week at this time of year from grateful guests.

Claridge's took the walkout in customary stride. "The spirit of Dunkerque reigned," the spokeslady said, under the oyster pink drapes in the restaurant, the band played. "Keep the home Fires Burning."

The Duke of Bedford insisted on making his own bed. Sir Sacheverell Sitwell made a point of coming in to sip aperitifs. Not a guest checked out and occupancy held at 93 percent. To demonstrate against "them," the rich willingly sacrificed the souffle, room service and midnight lobster thermidor.

After two weeks, the dispirited strikers voted to come back. Claridge's says it punished none, but it did give those who stayed on through "Dunkerque" a $55 bonus a week's holiday with pay.

The union, which claims it has 176 of Claridge's manual workers, is pressing still another govenment body, the Arbitration and Conciliation Service, for recognition as the hotel's exclusive bargaining agent. It also is backing Elvidge's plea to be rehired. The hotel, says management, will never be the same if the union wins.

Testifying for the management, Richard John Edmonds - reared at Clarridge's and now secretary to Boodles, one of the more snobbish clubs here - deplored the kind of training that a Grimsby Technical College gives an apprentice like Elvidge. A trainee might have only made mayonnaise three or four times he, said shaking his head sadly.