You should consider looking for a waste company that will collect all your general waste and separate it for you. its not a free-for-all waste type of thing, the way it is done is they drop companies into certain categories of waste. So they have an idea of all the main stuff that are dumped in your skip.
i.e. plastics, paper, composite, etc.
They uplift the skip as normal, and it’s then separated for that type of product accordingly.
There is a bit of come and go, but they can hit you with charges if you take the p*ss.
I use a local company, but companies like ENVA also do it, im sure. saves a lot of hassle with typical waste for the likes of sign companies, and as long as the waste company has the appropriate certifications, doing the separation and recycling responsibilities, it will tick your own boxes for doing the same.
https://www.enva.com