If you are feeling strongly enough about the medicinal blister packs (or anything else that doesn't seem to be widely recycled) to actually pay out money, or can persuade an organisation to sponsor collecting them for recycling, Terracycle provides these facilities.
I had a large carrier bag of blister packs, which I had started keeping a few years ago when I learnt that one of the pharmacy chains would accept them. My nearest branch was in the centre of town, and it was during Covid lockdown, so I waited until I had a bagful, then enquired about taking them in - no, they had withdrawn from the scheme! But I kept collecting - then heard that SOME branches of Superdrug would take them - but my nearest participating branch was in Stirling, too far for a quick bus trip.
I was starting to think I would have to just dump them when I found Terracycle. I think they primarily supplied big printed cardboard boxes for organisations to collect specific items for recycling - the cost of the box includes carriage and the cost of recycling, which in some cases has to be paid for as it doesn't produce enough return to be viable. However, they have recently introduced printed heavy plastic bags for smaller amounts, for individuals or small businesses, at lower prices. zerowastebag.co.uk/
It is £39 for a large bag (which holds a LOT A smaller one would have been £25) and when it is full I will take it to a locker at Tescos. My bag is currently in my local Community Centre, where it is filling up faster than I could fill it alone.
£39, or even £25, is quite a lot for an individual to shell out, but perhaps we need to put our hands into our pockets in the interests of global pollution by packaging? Many of us volunteer or have contacts with community organisations, maybe we could persuade them to invest in bags for a couple of categories and display them where those using the community can contribute?
They also have links to FREE recycling schemes run by various manufacturers for the things they make. For instance, there are some for contact lenses and solution bottles, toothbrushes, beauty product containers, crisp packets, Pringles packaging, cheese wrappers etc etc. www.terracycle.com/en-GB/brigades It is worth a look.