I should say "dustbin" is second only to "bin" in the UK. "Dustbin" perhaps favoured slightly by the older generations. Interestingly the reason we call it a dustbin is because people were used to being thrifty with their food, especially during the war and post-war years, and almost the only sort of refuse put out for collection was 100% inert dust and the odd animal bone ... people burnt or ate everything else. That all changed with the introduction of American style self service "supermarkets" in the 50s and 60s. Having previously been accustomed to shopping in small stores where produce was handed to them personally by an employee consumers demanded increased and more elaborate packaging to make up for the fact that goods may have been handled by other shoppers. More packaging and more unconsumed food made its way into our dustbins and they lost their dusty nature and became a deal more smelly.
Before plastic ruled the roost everything would go on the fire, the fire being a permanent fixture in the front room. If it was summer you would still have a fire in the evening.
The coal scuttle was a de-facto bin, anything that accumulated in there during the day went on the fire. This would also include the newspaper, which would be scrunched up to make a bed for the fire to be lit with.
It was perfectly reasonable to put things like vegetable peelings on the fire too. They might sizzle but they would still be gone.
Milk came in glass bottles that were washed out and collected by the milk man, very few other bottles were used, certainly no sugar drinks in aluminium cans. Tea ruled in England until relatively recently.
There was also the compost heap. So organic matter would go on there, not out of save the world principle, it was just the done thing. You would obviously eat everything you were given so it wasn't as if there were table scraps in the bin.
I don't believe consumers demanded more and more elaborate packaging. Since forever people have complained about excess packaging. It is actually all about cost. Take for example the recycled 'deposit paid' bottles of yesteryear. The glass was quite thick and they weighed quite a bit. Today glass is different, very thin, lightweight and hence cheaper to distribute. I would argue that packaging has became less elaborate - quality bottles of yesteryear have gone, as have proper biscuit tins to take two examples.
So, the dustbin, it wasn't random dust, it was whatever was left over from the fireplace, mostly ash from coal. Britain was an island of coal in a sea of fish in previous times.