As age continues to take its toll on Moscow's hierarchy, the just-concluded week-long visit here of 53-year-old Soviet Politburo member Mikhail Gorbachev has left most British officials and politicians impressed with the self-confident, rather easygoing manner of the man who may be the next boss of the Kremlin.

"He is recognizably a politician rather than a dictator, though he could end up being both," is the way Anthony Kershaw, the Conservative chairman of Parliament's foreign affairs committee, put it in an interview.

Gorbachev spent 90 minutes with Kershaw's committee and showed himself "to be in the same business as myself. He's flexible, a modern man, has a refined manner, seems in good health -- which is always important for a politician in Russia -- and makes points but doesn't hammer them.

"I would not have thought I could have talked to Stalin as I did to Gorbachev," Kershaw continued. "If Stalin wanted to reform agriculture he would have shot 10,000 kulaks. Gorbachev seems like he would hire 10 consultants."

As Gorbachev departed from Scotland yesterday, one day early because of the death of Soviet defense minister Dmitri Ustinov, the British government's minister for Scotland, George Younger, described the Russian's visit as "a very great success that ushers in a new phase in relations between Britain and the Soviet Union."

Whether that new phase gets further impetus remains to be seen. But judging from private and public statements made by the relatively few British government and industry figures who had more than perfunctory contact with Gorbachev, both Moscow and London seem pleased.

It is possible that the Soviets may be even more pleased because Gorbachev used the visit to emphasize Soviet demands to ban weapons in space and curb U.S. space defense programs.

After lengthy private talks with Prime Minister Margaret Thatcher, officials told reporters that Thatcher, too, was concerned about an arms race in space. While Thatcher apparently spoke in general terms and avoided criticizing Reagan's so-called "Star Wars" research program, the meeting nevertheless conveyed an impression that could create problems for Thatcher and a bonus for Moscow.

"The underlying effect of these discussions," The Times of London newspaper said in an editorial today, "was for the British prime minister to be used in a skillful piece of Soviet finesse which presented a worldwide audience with an appearance of affinity between the Soviet Union, Britain and her European allies, not just against the idea of the militarization of space, but by extension, against President Reagan's own specific plans for strategic defense against space systems."

On the other hand, Gorbachev's official comments here about Soviet attitudes toward reaching new arms control agreements were generally viewed as positive. And U.S. concerns about what did go on in the private Gorbachev-Thatcher meetings may have played a part in Washington officials saying more specifically later in the week that space defense programs were potentially negotiable.

Although Gorbachev visited Canada in May 1983, his trip here was the first close-up opportunity for the West to take his measure since he emerged more clearly this year with expanded ideological and foreign policy duties and as the probable heir apparent.

Kershaw and others say Gorbachev revealed nothing new about Soviet policy, and the Soviet leader reacted predictably, sharply and vigorously when committee members asked about religious persecution in the Soviet Union.

There were only a handful of demonstrators visible at the locations Gorbachev visited, although small but noisy groups protesting the plight of Jews and political prisoners in the Soviet Union dogged him at almost every stop.

What seemed new was the more modern face of would-be Kremlin leadership. The assessment that got most attention here was Thatcher's statement in a British Broadcasting Corp. television interview. "I like Mr. Gorbachev," said the hard-line British leader. "We can do business together."

"In the 10 years since she's been Conservative party leader," said one British diplomat later, "I cannot remember her ever making such positive comments about any East Bloc leader."

Gorbachev, as this diplomat put it, "seemed a man of self-confidence, not an apparatchik" who needs to fall back for instructions on every issue. "He had enough confidence to have other members of his 30-person delegation expand" on points and was not limited to official statements.

"He gave the impression of being more flexible in manner than in substance," the diplomat said of Gorbachev, and he was "not without some charm and affability." He was described as different from Soviet Foreign Minister Andrei Gromyko in the sense that Gorbachev showed "a willingness to debate points and to listen, though it doesn't mean he is a closet liberal."

Part of the positive reaction here also relates to the prospect of a boost for the British economy by expanded trade with Moscow. Once the major western exporter to Moscow, Britain now stands number nine, but Gorbachev said trade could rise by 40 percent to 50 percent in the next few years.

He talked of "the increased political role of business links" and told a chamber of commerce luncheon that big trade increases could not be achieved "without well-established and stable international trading relationships."

Visits to the Austin Rover automobile factory, the ICI chemicals group and the John Brown engineering company all brought hope of new contracts. The John Brown group, along with other European firms with U.S. licenses, had delivered U.S.-designed turbine generators to Moscow when Reagan was trying to enforce a boycott of the Soviet-West European gas pipeline project in 1982.

After Gorbachev's visit, a spokesman for the firm said the Soviet had told them that Moscow was "pleased that we had stuck to our contractual obligations."