SARS-CoV-2, as far as we know, originated in China, but more precisely around the wildlife market of Wuhan¹. In other words, a place that acts as an explicit interface between "populated" China and the wilderness parts of it. There are no similar markets in Europe¹ to my knowledge, though I suppose that our illegal pet/collectors' animal trafficking could serve a similar role.
Mad Cow (and later CJD) originated as - rather harmless - Scrapie, which was then introduced to cattle thanks to pretty shady livestock business practices.
So, neither entered the high-population world ready-made and under their own power, but were brought there by explicit human action, with our recklessness and/or ignorance (and all the obfuscation to cover that up) being major factors - and I have to admit that we're unlikely to rid the world, or even just Europe or a single nation in it, of those anytime soon ...
¹ While it's officially named a seafood market, which we certainly do have in Europe as well, the species suspected of having been hosts on the route to SARS-CoV-2 live on land, and I'm not aware of what effectly approaches "bush meat" getting anywhere near consumers alive here. Heck, Europe has called on China to outlaw such activities - how hollow a public statement would that be if we weren't doing it ourselves ...