Eagerly awaiting an update!
We have boxes for cardboard and paper recycling that are collected every two weeks. Each house is entitled to one box. We fill it in a week as they're so small.
The bin men literally pick them up, through the contents into a wheelie bin, then seemingly thrown them back to the ground with as much force as humanly possible.
One broke, so we contacted them and they said "you can have a new one but they're £13". Fine, I'll pay it. "OK - leave your broken one out and we'll collect it, along with its contents and leave you the new one". Great.
New one arrives, old one is not collected or emptied. So now we have two boxes - one of which is broken, one of which is shiny and new.
First collection, we go to bring the box in to find it split entirely down one side where it's been thrown so hard it's cracked.
Call them again "you can have a new one but it's £13". Not a chance are we paying for this. We've put it out once and your collectors have broken it on first use - it's not our fault. "OK - we'll send you a new one free of charge - leave your broken one out and we'll collect it, along with its contents and leave you a new one".
New one arrives, neither old one is not collected or emptied. So now we have THREE boxes - two of which are broken, one of which is shiny and new.
This third one survives the first collection, but not the second and now also has a big crack in it!
I've given up now, so have a huge pile of three broken boxes in the back garden, all of which are now mostly made up of Gorilla tape, holding them together. None of the lids fit because they're also broken, so they're held in place with a brick that one a really windy day becomes a very dangerous projectile!
The only benefit to them not collecting the broken box is that we now do at least have the ability to put all our cardboard and paper waste in them and we put out two every two weeks, rather than trying to stuff it all into the one we're supposedly allowed.
Back to big bins, OP, our council allows you to apply for a larger general waste bin if the household consists of 5 or more residents; or you have at least 2 children in nappies; or a resident has a medical or health condition that results in extra waste. We can do it online, so maybe check your council's website?