In the UK:
Every residence I've ever even been in/seen online has the washer (and dryer, if present) in the kitchen, or in a utility room which is as near as possible to the kitchen. I've never seen a 'laundry room'. The closest thing would be a utility room, but that usually has all the laundry stuff, plus tools, dog food, garden implements, basically 'heavy duty' or dirty things that you don't want in the main house.
(Utility rooms also don't always have a sink, and the sink is usually a 'dirty sink', for cleaning things like BBQ grills, I've never seen a special sink for laundry. )
To be honest, I've always thought that Americans make a huge pulaver out of doing a bit of washing. It's always depicted as some massive undertaking, with the need for a special room and all these special steps. (Sorting, washing, opening the lid to add rinse stuff, drying, folding...)
Everybody I know (including people with several young children) just chucks the clothes in the washer, takes them out, dries them, and throws them in the ironing basket until they can be bothered to iron them and hang them up (or if you're me, you just put stuff away when it's dry, I don't iron stuff unless I need to be smart).
The concept of 'laundry day', or needing a 'laundry room' is just silly to me, now that you can chuck it in the washer (which takes two minutes), and hang it out to dry (which takes 5 minutes). Even if I had several kids, I'd struggle to spend more than 20 mins a day on laundry, especially as most kids clothes don't need ironing.