A somewhat drifty sidenote, to show the phrase not entirely dead: when my late wife & I moved to this village 33 years ago, our originally cockney next-door neighbour {whom I saw recently and who is still alive in her 70s} mentioned in conversation with my wife that someone she knew had recently started a new job, for which she had received some advance payment; so that, she said "she is just working dead-horse at the moment".

Drifting even further, re another song: the same neighbour would always refer to buying second-hand clothes at a charity shop as "going to rag-fair".

~Michael~