Green’s Dictionary of Slang

a very short skirt.

1999		Roger’s Profanisaurus 3 in Viz 98 Oct. 16: greyhound n. A very short skirt, i.e. only one inch from the ‘hare’.
2000		personal correspondence: greyhound – a very short skirt. From the fact that a greyhound (on a racetrack) is close to the hare (hair), i.e. ‘Blimey look at the greyhound on that bird!’.
2015		L. McInerney Glorious Heresies 100: ‘Better than freezing your arse off in a greyhound skirt, isn’t it? [...] It’s a long-sleeved maxi dress’.