My understanding of false consciousness is that it's a false belief knowingly spread by others to achieve some aim. When someone justifies their political views as "just common sense" it's often an indicator because what's taken to be self-evidently true changes over time.

In my view, what matters is not so much the belief itself but the way in which it's reached. Let's return to the hospital example and assume that your local hospital is overcrowded and underfunded. If you look at immigration levels in your area, read about the economic impact of migration and the levels of government funding to your area and decide that, on balance, hospital overcrowding is due to immigration then I would not consider that false consciousness. Possibly incorrect, but not false consciousness. If you just see a lot of Romanians on the street and read lots of anti-immigration stories in your newspaper and conclude that the overcrowding is due to immigration then I'd consider that false consciousness because you are relying on a notion of "basic common sense" and haven't even considered the possibility that the migrants are contributing more than they take or that the government funding has been inadequate.

The whole questions of knowledge that we've been debating, though very important, is in a sense secondary to this because the person relying on common sense isn't actively dismissing the claims of economic truth, they're completely unaware of them.

And in this particular example I think it's pretty clear that the government sought to deflect anger at austerity to immigrants. Assuming that Cameron and Osborne shared the kind of elite worldview we've been discussing, they would have known that the deflection couldn't be justified. They were deliberately spreading a view of the world that, in their minds at least, they would have known to be wrong. So that's why I think it's false consciousness - knowingly spreading a false belief.

Where it gets complicated is when the elite come to believe the idea as well, and then it's just a received wisdom (and the original intent has completed succeeded). I think you're right to call out remainers' unquestioning belief that the EU is a good thing, though I disagree on how much we can rely on economic. You're right that we should be skeptical of that too, of course.

One important thing that neither of us has mentioned that much is the role of the media in propagating beliefs and the extent to which the British public's view of the EU has been shaped by the likes of Boris Johnson printing knowingly false stories about the EU ("knowingly spreading a false belief"...). I'd argue that all of these [1] are examples of false consciousness. Either the official figures are all totally wrong and a person looking down their street can make a more accurate estimate than teams of statisticians measuring the entire country, or views are shaped by distorted reporting of these issues. And if the media aren't trying to present a factual account of reality, that raises the question of what are they trying to do instead...?

[1] https://www.independent.co.uk/news/uk/home-news/british-publ...

Edit to add: I used to read the Telegraph but then they went down a weird spiral of clickbait mixed with making everything interesting premium-only. A pity because it used to be very good.