When staying at Weston-super-Mare as a child, she got lost and was only discovered when her mother heard her singing the Ernie Mayne hit, "An N'Egg and some N'Ham and some N'Onion".

[1][5] In 1963, Noël Coward created the part of the fish and chips peddler "Ada Cockle" specifically for O'Shea in his Broadway musical, The Girl Who Came to Supper.

Her performance of traditional Cockney tunes charmed the critics and helped win her a Tony Award for Best Featured Actress in a Musical.

[citation needed] In 1968, O'Shea was cast in the television movie The Strange Case of Dr. Jekyll and Mr. Hyde, which earned her an Emmy Award nomination for Outstanding Performance by an Actress in a Supporting Role in a Drama.

[9] O'Shea died of congestive heart failure at age 82, at her home in East Lake Weir, Marion County, Florida.