"A Girl Like You" (Edwyn Collins)

Scottish artist Edwyn Collins is another example of someone who is known for one song on this side of the Atlantic yet has had a lengthy career as a musician and producer in Great Britain.
Back in the late 70s, Collins founded the New Wave band Orange Juice, which--like New Wavers on this side of the Atlantic--took many cues from dance music (especially the band Chic), blending R&B rhythms with crunchy guitars.  Orange Juice also had the added element of Collins's sleepy baritone voice, which added a curious 1940s torch song quality to everything they did.  A perfect example is their biggest charting hit (in the UK), "Rip It Up."
Anyway, find and take a listen to Orange Juice's album Rip It Up (1982) sometime.  It's a solid set of 10 songs that explain where fellow Scottish band Franz Ferdinand got their sound.
"A Girl Like You" from his solo album Gorgeous George (1994) relies on a similar formula as his songs with Orange Juice: a heavy rhythm section, crunchy guitars, and his jazzy crooning.  Only on this occasion, he perfectly captures a swinging 60s, go-go boots and white shag carpet feel.
The rhythm track and bassline are actually sampled from a 1965 song called "1-2-3" by 60s US R&B/pop artist Len Barry.  Essentially, the entirety of "A Girl Like You" is built upon a 3-second snippet of the hippy-shake drums and bass from the intro of Barry's song, looped, over and over.  (Personally, I think it's a great use of a sample.  It doesn't smack you over the head that it's a sample at all.)
"A Girl Like You" also has Paul Cook, former drummer of The Sex Pistols, playing a groovy vibraphone line and Collins himself on fuzz guitar, which just radiates day-glo electricity.