A knack for sensing what the times demand; British royal traditionRoyal Family: Years of Transition, by Theo Aronson. Salem , N.H.: Salem House (distributed by the Merrimack Publishers' Circle). 271 pp. $ 19.95.

The British have pulled off a feat of considerable legerdemain during the post-colonial years: Less has in some ways become more. Although the empire folded its tents long ago, its language dominates the world; though Britain ostensibly has no more power within it than New Zealand, the Commonwealth is the largest group of states in some form of common association; and the monarchy, though stripped of most of its powers, is stronger than ever.

Theo Aronson's ''Royal Family'' is an admiring history of the successful transition made by the British monarchy from the reclusive reign of Queen Victoria to the present highly visible ''Royal Firm.'' The transition, never deliberately planned, has been largely the result of a combination of an immense sense of duty - the great Victorian legacy - and the remarkable characters of the monarchs and their consorts.

Queen Alexandra, the wife of Edward VII, brought into the family ''many of the traits that are there still: a taste for domesticity, a brand of knockabout humor . . .(and) an engaging naturalness.'' Alexandra's successor, Queen Mary, who saw her role as service to crown and country, gave the monarchy a sense of continuity, particularly during the abdication crisis. The warmth, sympathy, and encouragement of King George VI's wife, the present Queen Mother, gave the shy, nervous monarch the strength to become the king with the common touch. The qualities that endeared her to the British people are suggested by the remark she made to a policeman as she inspected the damage after Buckingham Palace received a direct hit during the World War II blitz: ''I'm glad we've been bombed. It makes me feel I can look the East End in the face.''

And Prince Philip has further broadened and modernized the monarchy, particularly by his insistence that the children be educated in a broad variety of public institutions rather than by private tutors in royal isolation.

The monarchs themselves have had the fortunate knack of sensing what the times demanded without ever entirely sacrificing the mystique that is still the source of the monarchy's strength and fascination. Aronson notes that Edward VII , with his wide European contacts, made a distinct contribution to British diplomacy, ''symbolizing Britain's abandonment of its posture of splendid isolation and its new commitment to Europe.''

His son George V, a blunt, unpretentious man, became the thoroughly British king who, like his fellow countrymen, distrusted all things foreign. He became the first monarch to visit the mining and industrial areas of Britain, forging links with the working classes rather than with the aristrocracy, something that further ensured the family's popularity. George VI's tenacity and courage particularly endeared him to the country during World War II, when he refused to leave London even at the height of the blitz. The judgment of his people was aptly summed up by a young workman: ''We all liked the king a great deal. Never wanted to be king, sacrificed everything for his country.''

Aronson is equally impressed with the present Queen, who in her already long reign has made the British Royal Family, he believes, more respected and loved than ever before. This affection, as the family shrewdly recognizes, is based on its position ''as a highly respected family institution standing above social and political faction,'' with a ''dynastic continuity'' that captures people's imaginations.

More accessible than her great-great-grandmother could have contemplated or endured, the present Queen recognizes that her being a representative of a glorious tradition is still one of the monarchy's greatest assets. The days of the divine right of kings are long past, but royalty must still walk a fine line between being just like any other respectable British family and being ''the underpinning of the other two estates of the realm.''

While just in his assessment of the contribution of the royal family, Aronson avoids any searching analysis of the family itself. One of the problems may be that, although the family has benefited in many respects from the vast publicity given it by the media, it has also become wary of being forthright. The family may have had no alternative, given the growing obtrusiveness of the news media: One of the obvious indications of the difference in the attitude of the press is that the British press made no mention of Wallis Simpson until a few days before Edward VIII abdicated, whereas royal romances today get plenty of publicity. The result, however, is a careful editing of personality and opinions.

''Royal Family'' is written more for uncritical fans and Anglophiles than for serious students of the institution. The tone is a shade short of fulsome, the historical and biographical details are repeated with the respect of a true and loyal subject, and the conclusions, if just, are predictably complacent. And Aronson's final judgment is remarkably apt: ''What other country can nowadays christen an infant knowing that it is likely to become its king in two generations' time?''