When she was a child, she liked to turn cartwheels and be called Sandra. Her ambition was to be a circus bareback rider.

She did become an accomplished horsewoman, but these days, don't call her anything but "your royal highness." Because Alexandra Helen Olga Christabel, Her Royal Highness Princess Alexandra, Hon. Lady Ogilvy, GCVO, has a richer royal pedigree than the Queen of England.

When Princess Alexandra arrives in Southern California this week to lend the British Royal Family's presence to the Festival of Britain in Orange County, residents will get a look at not only the queen's first--and favorite--first cousin, but a descendant of King George V, King Edward VII, Queen Victoria, King George I of Greece, King Christian IX of Denmark and the ill-fated Czar Alexander II of Russia.

Although she is unknown to most Americans, in Britain, Alexandra is the most popular and accessible of the royals.

Throughout her adult life she has taken on the role of what has come to be known as the "professional princess," representing Britain and the Royal Family at official engagements at home and abroad.

She wears the royal mantle lightly, however.

She is " . . . a woman of unstuffy charm and classic beauty, regal in presence but highly accessible," author Ralph G. Martin wrote in his book, "Charles and Diana." "When she was Diana's age, she was also known as a marvelous dancer, a gay conversationalist who loved to laugh, adored children, had a craving for sweets and was a ballet addict. Her favorite jazz piece was 'Ain't Misbehavin.' "

But in her professional role, "she's got an enormous interest in whatever she's doing. That's the main thing that comes across," said Sir Eldon Griffiths, a member of Parliament who lives part time in Orange County, lectures at UCI and is the president of the county office of the World Affairs Council. "She does her homework and she's very well briefed. She, in fact, goes at it very hard."

The princess visited Los Angeles in 1971, in connection with a promotion of British menswear. She will return briefly after her Orange County visit--next Monday and Tuesday--to, among other things, meet with Mayor Tom Bradley, visit Union Avenue Elementary School and observe a program for mothers of children born with a crack addiction at County Harbor/UCLA Hospital.

Mona Mitchell, the princess' private secretary, said in a telephone interview from London that Alexandra was delighted by her last visit to Southern California and "thoroughly enjoys travel."