The PE lined coffee cups are recycled in the UK, and there is a mandatory cup takeback scheme coming in over the next couple of years to help increase recycling rates.
> There are five facilities in the UK that are able to accept polyethylene lined paper cups for recycling and together have the capacity to recycle all the cups consumed in the UK annually.
https://www.jamescropper.com/about/innovation/coffee-cup-rec...
https://www.valpak.co.uk/case-study/national-cup-recycling-s...
> There are five facilities in the UK that are able to accept polyethylene lined paper cups for recycling and together have the capacity to recycle all the cups consumed in the UK annually.