I think you're barking up the wrong tree by looking for murders involving a barrel. In the passage you quote, the context is about the notion of clergymen being immoral, "naughty" as she puts it.
The reference then would be to Harold Davidson, also known as the "Rector of Stiffkey" or the "Prostitutes' Padre". He was a rector) who was prosecuted in court for immorality, accused of associating with "women of loose character", and "accosting, molesting, and importuning young females for immoral purposes". After his conviction and defrocking, he paraded himself in a barrel on the Blackpool seafront in order to earn money for his defence campaign.
All of this happened in 1932, so it would have been in recent memory at the time _Three Act Tragedy_ was written. (I found it by searching the web for "vicar in a barrel".)