Some places to recycle stuff that might help, OP, because not everything can just be put in the magical wishcycling bin:
Contact lenses and cases: opticians should have a bin for these. We keep a bag on the back of the bathroom door to collect them.
Soft plastic eg carrier bags, post bags, some film from fruit punnets, cereal bags, etc: supermarket soft plastic collection bin. Another bag hangs on the kitchen door for these. (Life now is just bags hanging in various places.) We’ve stopped buying anything where the film isn’t recyclable.
Paracetamol and medicine packets: Superdrug pharmacy will take these. Quite grumpily, but they’ll do it! Another bag hanging off another door!
Fabric, such as outgrown kids’ pants: the tip. Make a regular tip run part of your life! If you’ve got nice neighbours, take some of their stuff sometimes and they’ll quid pro quo. Especially if the bin men won’t take extra kerbside recycling as ours won’t, as if it’s not in the green bin it can be contaminated/wet and fuck up the whole lorry load. General waste doesn’t go to landfill anymore, it’s burned for energy production.
General recycling: primary schools and playgroups round here are forever asking for stuff to do junk modelling. There is also a thriving eBay market for old Bonne Maman jars and, weirdly, bulk lots of cardboard loo roll tubes. You do need the space to store till you have loads, though. We use yoghurt pots and plastic punnets everywhere as drawer organisers for stuff like calpol sticks; don’t think I’ve recycled one in years, there’s always something to put in one in a cupboard.
Bit of cash upfront but switching to reusable silicon mats and lining papers instead of greaseproof paper if you bake, beeswax fabric wrappers instead of foil or clingfilm, reusable covers for leftovers (also cuts down food waste). So no wods of clingfilm in the bin or the tube/box in the recycling.
It is much harder if your council doesn’t collect food waste – and I don’t think all of the posters here are acknowledging that – and you don’t have space/scope for a compost bin – our road is very foxy, ratty and seagully so composting requires lots of upfront investment to ensure the food scraps don’t get dragged up and down the twitten. We’ve managed but not all our neighbours can; most of the black bin stuff is food. A wormery can be a good alternative!
What else? Tissues can’t be recycled but if you accidentally run them through the washing machine every single time then put the wet wodge on the radiator, it’s much smaller!
Lead the way in not doing party bags when you reach that era, less tiny non-recyclable crap to go around. Give up kitchen roll. Use bar soap in a paper wrapper instead of liquid soap in a plastic bottle, much less space in the recycling.