Good to see that this forum isn’t afraid to get to grips with the controversial stuff…
Dressing gown! A housecoat is a different animal, as @Wildflower describes. They were worn for doing household chores like laundry, dusting, laying coal fires, scrubbing the front step etc.
I say house coat all the time! Although it’s only through habit! I find scousers say it all the time, especially the older ones! I used to take the mick saying it and it stuck with me I do believe it is a dressing gown they are referring too though