Originally envisioned as a ballad, "Girl Don't Come" was ultimately recorded at the tempo of Shaw's first hit "(There's) Always Something There to Remind Me". Shaw disliked this arrangement of the song and had to be persuaded to record it, preferring that it be relegated to the B-side of another track, the Chris Andrews ballad "I'd Be Far Better Off Without You". Shaw's manager Evelyn Taylor favoured "Girl Don't Come" but acquiesced to Shaw's wishes. However, when Shaw performed both songs on a British television show, "Girl Don't Come" drew the best reaction and radio airplay: it was as "Girl Don't Come" that the single entered the UK Top 50 (dated 12 December 1964) to peak at No. 3 in the week of 23 January 1965.

Although not one of Shaw's three UK No. 1's, "Girl Don't Come" is widely regarded as Shaw's signature hit and – unlike "Puppet on a String" – the singer has grown to appreciate the track to which she initially had an aversion. "Girl Don't Come" has also been recorded by Debby Boone, Cher, Ronnie Dyson (as the B-side to "(If You Let Me Make Love to You Then) Why Can't I Touch You?"), Eddie Rambeau and Ronnie Spector.

"Girl Don't Come" gave Shaw a No. 2 hit in South Africa and in Canada. In Australia, the song reached No. 48. Like "(There's) Always Something There to Remind Me", "Girl Don't Come" became a regional hit in the U.S. – where it was released in February 1965 – without entering the [Top 40], although it reached No. 42 on the Billboard Hot 100. Shaw was unable to do U.S. promotion – including a Shindig! appearance scheduled for March – due to the U.S. Federation of TV and Radio Artists refusing her an American work permit.

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