Any questions has a long history of its own - it started in 1948
according to Wikipedia it was perhaps the model for the BBC Television programme "Question Time" and is very similar in format.
Down your way was a very different type of programme
https://en.wikipedia.org/wiki/Down_Your_WayDown Your Way was a BBC radio series which ran from 29 December 1946 to 1992, originally on the Home Service, later on BBC Radio 4, usually being broadcast on Sunday afternoons. It visited towns and villages around the United Kingdom, spoke to residents and played their choice of music.