My mother was a regular listener from the start in the 50s, but less devoted once the telly came along to fill the long winter evenings instead. In the 60s and 70s when I was growing up, we often heard the first bit of the omnibus on Sunday mornings before leaving for church (racy tune, Tom Forrest's little homily, bacon frying...). In the school holidays (my mum was a teacher so they were her holidays too), if we were at home on weekdays she would usually have Radio 4 on in the background while cooking, washing up etc, so we'd often hear the lunchtime repeat.
I don't remember paying attention to any of it back then, but of course it was all very familiar when I got drawn into it myself in the very early 80s. Mum's radio station of choice nowadays is Classic FM, sadly, so we only ever talk about TA if there's a national news story about it. Pity.