The new general secretary of the Central Committee of the Communist Party of the Soviet Union has already served notice that he is going to challenge President Reagan in his two strongest suits: affability and public relations.

The raves about Mikhail Gorbachev are coming not from satellite lackeys or nervous Third Worlders. To the irritation of the White House, they are being spoken in the crisp diction of the numerous public figures who met him during his week-long December stay in Great Britain.

Reagan's greatest fan, British Prime Minister Margaret Thatcher, spent six hours with the Soviet visitor and afterwards jolted her country and ours by volunteering that she liked him and felt that they could do business together. The prime minister explained that it was possible to talk to Gorbachev, to exchange ideas without being pelted with the slogans and tirades that are the usual conversational gambits of old-school Soviets.

During his London visit, Gorbachev met almost every major politician in England and gave most of them the impression that he is a practical sort of a chap. They had the feeling that the minister of agriculture was not so much interested in burying the West as in learning from it everything he could about ending the profound embarrassment of the Soviet Union's inability to feed its people.

He turned nasty only when a member of Parliament pressed him about the cruel treatment meted out to dissidents. He told him to mind his own business.

The British gushed over him and his slim, stylish English-speaking wife. One Brit went so far as to compare the couple to Jack and Jackie Kennedy. Actually, Gorbachev looks more like the late senator Joseph McCarthy, and nobody gets to the top in Moscow by following the Golden Rule.

His smash success in London may have been the critical factor in the Politburo's decision to choose a youngish charmer over one of the stony-faced elderly gentlemen in certifiably bad health and badly cut overcoats who generally are selected to lead the Soviet Union.

Gorbachev comes across as a plausible and focused individual, with an enormous potential as a wedge-driver in the West. He threatens Reagan with his first real competition on the world scene. He is not dismissible, as Reagan seems to realize. He tried to cover his failure to attend Konstantin Chernenko's funeral by issuing a summit invitation to the new leader.

Gorbachev's views on arms control were partially revealed in London, where he argued against "Stars Wars" research. But his grasp of public relations has been demonstrated. His negotiator in Geneva, Viktor Karpov, went toe to toe with our man Max Kampelman for television coverage and walked away with it.

Karpov was shown chatting genially with Western reporters. Yes, he was representing his new leader on arms control -- the position had been approved weeks ago. No, the Soviets did not wish to let Chernenko's death interfere with the opening of the talks -- they were too important. Kampelman merely said that in the first meeting the Americans and the Soviets had agreed to respect the "confidentiality of each side." The East, in other words, was talking; the West was not. Advantage, Mr. Karpov.

Gorbachev's first speech to the Central Committee was impeccable, free of anti-American ranting. He said he shared the dream of the eventual elimination of nuclear weapons.

There was divided counsel within the White House about the president's attendance at the funeral. He said that was too busy -- too much on his plate, he put it inelegantly.

He had been told that by going he could meet the universal mood of relief and hope that an armed and dangerous nation had finally chosen a vigorous, 54-year-old pragmatist to take charge.

Richard Viguerie of the New Right fired off a preemptive news release, urging the president not to go.

But it was a chance to show good will to the new leader, to push along the possibility that change is in the air, to demonstrate that his foreign policy consists of more than Soviet-bashing.

Reagan has been having a free ride on arms control. He is using Geneva as a reason to increase the defense budget, vote for the MX missile and continue the arms race.

If Gorbachev is serious, he may make a proposal that will force Reagan to get down to specifics on arms control. Already Reagan knows that anti-Soviet rhetoric will not be enough in dealing with the new sharpy in the Kremlin.