NOT FOR the first time, a Western public is pinning a clutter of hopes and, almost certainly, foolish illusions on an unknown new personality in the Kremlin. A few years ago it was Yuri Andropov, hailed in some quarters as a likely closet liberal -- the proof was that he supposedly drank Scotch and liked jazz. In power, he turned out to be what you would expect of a man who had run the KGB for 15 years.

Now a new Kremlin figure has caught Western fancy. He is Mikhail Gorbachev, the Politburo member currently visiting England, where his relative youth (53) and quickness on his feet and his wife's clothes and smile have made him a lion. From Prime Minister Thatcher on down, distinguished Brits pronounced themselves charmed and suggested that, if Mr. Gorbachev is duly promoted, a new day may dawn.

To be sure, a few sourpusses noted that when Mr. Gorbachev was challenged on a human rights issue he replied with the Soviet elite's familiar defensive snarl. Nor could his single-mindeded pursuit of his evident political mission be entirely ignored. The Russians are attempting to work over Western public opinion by way of gaining advantage in the talks that the Soviet and American foreign secretaries are to hold in Geneva in January. To this end, Mr. Gorbachev played adroitly on the hesitation verging on disenchantment toward the American "Star Wars" proposal that is widespread in the British government and elsewhere in Western Europe. He also tickled the left with the fantasy that negotiations could conceivably move toward the prohibition and eventual elimination of nuclear arms.

If you think about it, it is no real compliment to the Russians to ooh and ah over their nice suits and their pleasant manners. The praise betrays the common presumption that they are boors. What must the Russians think, however, to see this indication of the fickleness of Western public opinion, of the impressionability of important people, of the desire to please and be pleased?

Perhaps no one on either side is fooled by these little interludes. Certainly there is no shortage of frosty moments and ill humor between East and West. Still, it should be possible to compose a public attitude that is consistent and rational and not subject to the tugs of superficial fashion.