Your initial statement just mentioned bottles, not cans. Total plastic recycling is significantly lower than the overall packaging recycling rate. With bottles making up such a significant portion of plastics, the numbers don't suggest high rates of recycling. Let's face it, if the recycling rate was anywhere close to the targets they wouldn't have introduced this scheme in the first place.
Pizza boxes:
Your takeaway pizza box can go in the recycling bin, even if it has grease on it. But if there is any part of the box that is contaminated with food, tear it off and place it in the food waste bin.
Coffee cups have a lining that mean they are not recyclable, they are generally compostable and will state such on the side, but really only in commercial composters.
While I'm not a fan of deposit schemes, many other countries have shown them to be successful. What do you think is required reverse falling recycling rates to ensure we meet our targets and avoid fines, and how much would that alternative cost?