Green’s Dictionary of Slang

a rest, a moment of relaxation; usu. in phr. (have) a Bex, a cup of tea and a lie-down, relax.

1985		R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 27: He had two have two Bex powders, a cup of tea and a lie-down.
1986		R. Beckett Dinkum Aussie Dict. 3: A Bex, a nice cup of tea, a cry and a good lie down: A somewhat archaic phrase, usually directed by a woman friend to a woman sufferer.
1999		Medical Journal Aus. 🌐 [headline] A cup of tea, a Bex, and...
2003		‘A site on the World Wide Reb’ in PC Update Jul. 🌐 Phew! Sit down and have a Bex if you need to. It gets easier from here.
2012		abc.net.au 19 June 🌐 Gee Moniker....talk about drawing a long bow.....take another Bex Powder and have a lie down before you blow your racist poofle valve!