The club certainly exists, as I received my first order last week

You can try visiting www.britishairwayswineclub.co.uk but you'll find it's just a link to Laithwaite's, who run the club in association with BA. It's all very UK oriented - not at all sure that it will work if you are based in SYD.

Can definitely confirm that bonus miles are part of the picture

Maybe someone with more experience of the service can comment further.