In February 1963 Davis had her biggest success with a cover version of The Exciters' "Tell Him". Written by Bert Russell (also known as Bert Berns), this song was covered in the sixties by a number of artists, including Helen Shapiro and Alma Cogan, and was successfully revived in the late 1990s by Vonda Shepard, for the American Fox television program, Ally McBeal. Davis' recording reached number ten in the UK chart, and was followed by "He's The One", which crept into the Top 40 in May 1963.
In 1963, the year in which popular music was transformed by the rise of The Beatles, Davis left Decca records due to financial disagreements. In September of that year she suffered a broken jaw when a chauffeur-driven limousine in which she and Jet Harris, former bass guitarist of the Shadows, were returning from a concert in Worcester crashed in the West Midlands. Harris received head injuries that seriously affected his already troubled career. The reporting in the press of a relationship with Harris, an unhappily married man, earned Davis, still only 17, some unwelcome publicity at a difficult time and may have been one of the factors which held back her career. In an interview included in the liner notes of the 2007 compilation CD Whatcha Gonna Do? (RPM 326), Davis acknowledges the scandal, but also places blame for the "lost momentum" on being unable to record for four months due to having her jaw wired shut after the accident.