Sarah Churchill, whose flamboyant style of life overshadowed her acting career and sometimes dismayed her father, Winston Churchill, died early today after a long illness, her family said. She was 67 years old.Her brother-in-law, Lord Soames, said she died in her sleep at her London home after an undisclosed illness. Funeral arrangements were pending.  The death of Sarah Churchill, who had lived in the United States for more than 20 years, leaves her younger sister, Lady Soames, as the only surviving child of Britain’s wartime Prime Minister. Diana died in 1963 and Randolph in 1968.Sarah Churchill, who became Lady Audley when she married Lord Audley, her third husband, described in her 1981 autobiography, ”Keep On Dancing,” the ”wild period” that took her onto the Broadway and London stages and through her three marriages, drinking bouts and wild parties. ‘The Lamb Who Strayed’

In an interview last year with The Standard, she described herself as ”the lamb who strayed from the fold.” Lady Audley said she grew up as a loner. ”I had a lovely childhood, but I suddenly knew around 17 I had to make a break,” she once said. ”It was too comfortable, too secure.”After leaving school she studied ballet and made her first appearance on the stage at the Adelphi Theater in London at the age of 21 in the chorus line of ”Follow the Sun.”

She fell in love with Vic Oliver, an Austrian comedian 17 years her senior who was associated with the show. They married in 1936, much to her father’s distress. Worked in Photo Intelligence   When World War II started, Lady Audley left the stage and worked in photo intelligence for the Women’s Air Force until 1945. She took two short breaks to accompany her father to the 1943 Teheran conference with President Franklin D. Roosevelt and the 1945 Yalta conference, where Churchill, Roosevelt and Stalin mapped postwar plans.

She was divorced at the end of the war. She made her first appearance on the American stage in Princeton, N.J., in 1949 as Tracy Lord in ”The Philadelphia Story,” and later toured in the same part. That year she married Anthony Beauchamp, a photographer.

In the 1950’s she was often seen in dramatic roles on American television. She also appeared in ”Gramercy Ghost” on Broadway, in the title role in ”Peter Pan” at the Scala and toured Britain as Eliza in ”Pygmalion.”

Mr. Beauchamp died from an overdose of sleeping pills in 1958. Friends said she finally found peace with her third husband, Lord Audley, but he died in 1963 within a year of their marriage. She had no children from any of the marriages.   She last appeared onstage in 1971 and had devoted the last decade to writing, entertaining friends, reading spy thrillers and watching old horror movies.