What's the meaning of the phrase 'Billy no-mates'?
Someone with no friends.
What's the origin of the phrase 'Billy no-mates'?
Coined in the youth culture of the UK in the 1990s. This sort of naming became widely used by the UK's young following the popularity of comedy performers like Harry Enfield, Paul Whitehouse, et al. Their comedy uses named character types, e.g. Tim Nice But Dim, Checkout Girl, Unlucky Alf.
The first explicit reference in print I can find is from the (London) Daily Mirror's preamble to the 1996 Oxford/Cambridge University Boat Race, by Jane Johnson and Carole Aye Maung, in the Mar. 27 1996 edition. It was headed 'NICE LADS, SHAME; ABOUT THE BOAT RACE ; Our oarsome guide to varsity blue-eyed boys' [in a pun in the sexist comment - usually directed at women - 'nice legs; shame about the face'].
Each rower was given a potted biography, including:
Phww-oar rating: 3.
Nickname: Billy No-Mates.
Personal file: 21, 6ft 3ins, 12st 11lbs.