Apart from Band Waggon, you mean? That was the BBC's very first regular comedy show - actually it was predominantly a music show, with Jack Hylton's band and singers, with about ten minutes, total, of comedy.
It was going to be cancelled, so Askey and Murdoch took over the wrioting, and it became an enormous success. I've not, so far, come across another Askey radio series - Arthur was a very early TV performer - even for Logie Baird's mechanical system - and after WWII was very creative in that field.
Before Your Very Eyes was the title of one such series. His daughter, Anthea, did work in radio in at least one series I recall, Wrinkles with Tom Mennard and Ballard Berkely.