Your local Council web-site is accountable and should tell you exactly what happens to your kerb-side collections. I keep meaning to make a visit to the local recycling system, when we drive by it I remember

: by the time I get home

I have always put used kitchen roll on the compost bin, as I do most paper and cardboard. Media companies are now wrapping magazines in rottable plastics ....... I have a small corner in our home composting heap to see what does rot after a couple of years

by which time plastics will be improved.
Toilet roll and kitchen roll inners
Letters
Soft boxes
Peelings
Tea/coffee
Stopped buying tea-bags when we discovered that the bags don't rot
Newspapers go into the kerbside collection.
Thick cardboard
Weekend magazines