The episode, named “The Marriage Bureau” aired just once, on 8 February 1955, attracting an audience of 6.22 million listeners, according to the British Comedy Guide.
The news was announced by the Tony Hancock Appreciation Society on Twitter, who wrote: “We’re absolutely thrilled that a lost episode of Hancock’s Half Hour has been found, restored, and will be broadcast on Radio 4 on 18 October.
“‘The Marriage Bureau’ was never repeated and has not been heard since 1955. Only episode to feature Peter Sellers,” they continued.
“Sellers plays the parts given in the scripts to Kenneth Williams who couldn’t make it that week. How did he play them? Tune in to find out! This is a brilliant find!”
The society added that a documentary about finding the lost episode, called Raiders of the Lost Archive, will be broadcast on Radio 4 on 13 and 17 October.
Hancock took his own life in Australia on 25 June 1968, in a rented apartment in Sydney, aged 44.
Hancock's Half Hour was first broadcast on radio in 1954, then on television from 1956, drawing an audience of millions every week.
Hancock played an unsuccessful music hall performer and minor stage personality, frequently ripped-off by Cockney conman Sid James and beset by the idiocies of an array of supporting characters, all voiced by Williams.