As Cheapbread said, Mam/Mammy/Mami in Wales. It's cultural, from the language.
In Ireland it's Mam or Mammy, or Mamaà or Maim among Gaelgoirs, to quote Cheapbread " It's cultural, from the language." Or was. Anything else has been 'acquired'.
Squoosh, " I absolutely cringe when adults refer to their mother as Mammy." Do you also cringe at the Welsh usage of Mammy or Mami? If so, why? And what makes 'mum' and 'mummy' so superior? Is it because they are derived from culture and language which you regard as superior?
JapaneseMargaret, I had to look up the word 'schlocky' and it means cheap or trashy in yiddish. Why do you call 'mammy' cheap and trashy? If they use the word 'stairs' in Mrs. Brown's Boys, does that make the word 'stairs' cheap and trashy? Mammy does have a usage outside of a sit-com. I know a lot of lovely and fine adults who call their mother 'mammy'.
I must admit, having been reared in Conamara, the only people I heard use the term 'mum' growing up were children of people who had emigrated to England and returned home with their families. A lot of families returned home when the economy improved (and social welfare increased in Ireland). When I was growing up we only received Irish tv stations (not bbc). Maybe as the economy exploded and people were exposed to more Anglophone media the usage has been 'acquired'. Maybe people with pretensions reinventing themselves too, and in their thinking it makes them appear a little bit 'cooler'. It certainly has no origins in Conamara. I have family there who the term would be absolutely foreign to (both Irish speaking North and English speaking south), so can't be that common. Mind you, some parts of my family don't speak English to each other, so are hardly going to use 'mum'. It would be as natural to them as 'mutti'.
Mum may be used in other parts of the country, but I don't know about common. I think stating it's 'common' is over egging the pudding. I suspect, if you go back even one or two generations from a lot the people who use it today in Ireland, it was not used in their families. The very common 'Mam' or 'Mammy' would probably have been overwhelmingly used. Now, I understand as we are exposed to a huge Anglophone culture through media which we were not exposed to before, so it is easily acquired and becoming more common. And maybe those most susceptible to consciously acquiring it are people who perceive it to have a 'cooler' vibe because it's not humdrum homegrown, certainly among people who place less value on any remnant of our own culture. Or people just unconsciously imbibing it.
I have a relative (Gaelgoir) who got her daughter to call her 'Mamma' and the father 'Pappa'. Don't know how common that is in Dublin, but it's the first generation usage in our family and certainly acquired. They did proceed to go and live in a Francophone country though. (funnily, it wasn't Maman and Papa). I don't think the fact that I can refer to someone who uses 'mamma' and 'pappa' in Ireland gives it validity as common usage though. However, trends change and 'mum' and 'mummy' may grow more common is usage as Irish people are more exposed to them and they could replace the more traditional terms.
Just for the record, I know a lot of lovely and fine people (adults and all English) who call their mothers 'mum' and 'mummy'.