LONDON— ''The Tempest'' has always been one of Shakespeare's most popular plays. It also possesses a mythical power that seems to inspire other artists. As the Shakespearean scholar Anne Barton points out in the New Penguin edition, Mozart sketched out an opera based upon it, Hollywood plundered its story for a science fiction film (''The Silent Planet''), T.S. Eliot used fragments of it in ''The Waste Land'' and W. H. Auden wrote a long poem, ''The Sea and the Mirror,'' dwelling on the destinies of its principal characters.

But it has never enjoyed such a theatrical boom as it did in 1988 when playgoers in Britain were confronted by no fewer than five separate productions of the play. Peter Hall, who made his debut with it at the National Theater in 1973, ended his 15-year directorship with a radically different version. John Wood is currently playing Prospero in a Royal Shakespeare Company production at Stratford-on-Avon, which will later transfer to London. Jonathan Miller directed the work at the Old Vic with the screen's former exorcist, Max von Sydow. Tokyo's Ninagawa Company imported a boldly theatrical version to the Edinburgh Festival last autumn, and Cheek by Jowl, an innovative London-based touring company, is currently performing the work in repertory with Sophocles' ''Philoctetes'' (another play about a desert island hero).

Shakespeare once defined love as a quality that ''looks on tempests and is never shaken.'' In 1988 playgoers in England and Scotland looked on more ''Tempests'' than ever before. Whether they were shaken is another matter.

Why should there be so many productions in one year? In part it is a reflection of renewed interest in Shakespeare's late plays. Once seen as fairy-tale romances with a Tennysonian aura, they are now viewed as much tougher, harsher plays in which Shakespeare balances his preoccupation with loss and recovery with visions of unregenerate humanity.

Even the much-maligned ''Cymboline'' turned up both in Mr. Hall's season of late plays at the National and at the R.S.C. and proved itself not to be the hodgepodge so disliked by Dr. Johnson and Shaw but a boldly experimental play about sexual torment, national discord and the good and base aspects of humanity.

But the real reason for the popularity of ''The Tempest'' is not hard to see. In an age of director's theater, it allows every interpretative artist to conjure up his or her own world on stage just as Prospero controls the elements on his enchanted isle.

Indeed the play can be seen as a metaphor for the theatrical process itself with Prospero equipping himself with the artist's power to raise the winds and darken the sun, shake the earth and command spirits while at the same time confronting the dangers of playing God. It is no accident that two of the recent productions (the Ninagawa Company's and Cheek by Jowl's) both seized on the idea of a play-within-a-play with Prospero presented either as a benevolent impresario or a dictatorial surrogate-author.

Paradoxically, although ''The Tempest'' is a director's play, the most striking feature of the recent productions is the drastic revision of Prospero as a character. Stage tradition usually sees him as a benign schoolmaster or a wizened sage who is a mixture of Santa Claus and Michelangelo's Noah and approximately four times as old as his brother Antonio.

Michael Bryant at the National, however, played Prospero as a tetchy autocrat turning purple with fury at the mention of his brother and looking back in anger at his usurpation. When he described to Miranda how the two of them were ''heaved'' out of Milan, Bryant leaned on the verb as if still obsessed by his humiliation.

But the major insight of both director and actor came in Prospero's famous renunciation of his magic: a speech often taken on a rising melodic curve so that we ignore what is being said. When, however, Bryant came to ''Graves at my command have waked their sleepers, oped and let 'em forth by my so potent art,'' he stopped dead in his tracks as if haunted by his practice of Faustian necromancy. And when he ''required some Heavenly music'' (an achingly long time in coming), it was in the tones of a diabolist urgently seeking absolution.

Mr. Wood, returning to the R.S.C. after a gap of 16 years, also got away from the idea of Prospero as an old conjurer in decreasing demand at Masonic banquets. In his open-necked shirt, baggy trousers and gardening boots (what else would he be wearing after 12 years on a desert island?), Mr. Wood presented us with an angry hermit who uses supernatural power to shield himself from human contact.

Prospero lost his dukedom, Mr. Wood forcefully reminded us, because he was ''all dedicated to closeness,'' and you sensed his tormented, bookish solitude in the nervous jocularity with which he greeted his old enemies and in the tentative way he donned his restored crown. But Mr. Wood, as the most exciting Prospero of the year, also invested the character with a wealth of sardonic irony. When Ferdinand assured Prospero that Miranda's ''virgin snow abated the ardor of his liver,'' Mr. Wood greeted his reassurance with a deeply cynical ''Well,'' as if he had heard that one before.