Western meat production isn't unsustainable, at least not the one run in Europe. If the production method used in USA is unsustainable then it is only because you have so much space that you have more environment to ruin, if it looked like Europe where you don't have more nature to ruin you'd adapt meat production to become sustainable. It makes meat a bit more expensive in Europe but people still happily pay and eat it.
I don't see the problem? UK is a densely populated island. Mainland Europe has way more land, it makes sense for them to import. Or do you argue that UK shouldn't eat meat since they don't have enough land for it while mainland Europe can eat meat just fine since they do have that land? We trade between nations for precisely this reason!