You have a big bin and still have so much rubbish. What on earth?
We are a family of 4 and have a standard size bin. We rarely fill the bin, don't go out a lot due to affordability on top of all the extra clubs and tuition. Do you practice recycling? I can't help but wonder what this excess rubbish is and ifyou are constantly shopping and spending money, maybe you should pay to cart some down to the tip or walk to the local recycling hub.
I also wonder when your LA plan to give you all the extra bin where you are expected to separate your genral waste from food, garden, paper, and plastic/glass waste.
Re: social services, they have better things to spend their stretched time on. I suspect the most that will happen is that it will be repored to environmental health, and you can highlight the lack of collection, which is their remit. As you are picking up fox stren rubbish, it shouldn't go any further. Stop worrying, it hasn't happened yet. Worse case scenario, someone turns up on the door, tell them no comment and you will speak to them once you have obtained adequate advice. Don't let any one in your house, you are not obliged to. Don't give out school info, and just contact Citizens Advice for more information tailored for you. Seriously though, assess your consumption, cause it sounds crazy.