In summary: I agree! I also live in London.
To take your specific examples, I know of two fairly local establishments that have game licenses, but I haven’t seen a wild rabbit in either that I remember (I’m not a big fan of rabbit, so I wouldn’t look out for them); I don’t think I’ve seen a hare since 2000. All they have are pheasant and partridge, sold oven ready and usually not hung long enough because people get squeamish if they get a faint sniff of that old cheese smell. While I’m not an advocate of hanging game until it is “high” I think folk buy them once because oven ready but never again because they are tough and tasteless prepare like that. I think people are generally squeamish about eating “bunnies” these days.
Back fat, slab bacon etc – I can get back fat if I really want it, (try Morrisons supermarkets in England) but even the good butcher gets his excellent bacon in pre-sliced and pre-packed; at least it is cut to the right thickness, not the wafer-thin stuff often found. I think the problem is, as you say change in the supply chain, so few butchers get whole carcases now, those that are make a virtue of it and charge accordingly (the MEAT small chain in London for example, very good). If you can get out into more rural areas farm shops are sometimes a good source of the of odd bits. Or covered markets when visiting other towns.
I do agree it’s a change in the way recipes are presented and used too, mayonnaise, lardons, and pulses for example are all assumed to be bought ready to use and there is no alternative or suggestion that you might not just open the jar, packet, or can. I saw one cook writing in a magazine get quite panicky about what to do if you couldn’t buy lardons, apparently she thought attacking bacon with a sharp knife would be beyond her readers, though that’s what I did for my first 30 years of cooking.
I’m hoping the idea that one 400g can of beans is right for any recipe soon goes, like many people now I have an electric pressure cooker (mine’s an Instant Pot mini) and it is no more trouble to cook just the right quantity of pulses on an automated setting than to open a can or two, or an overpriced jar of Posh Pulses. One day I’ll find a pack of dried flageolets again in London, one day.