You can actually see the same dynamic playing out with Swiss access to the EEA: https://www.euronews.com/2021/05/27/what-s-the-future-of-eu-...

The debate doesn't seem to be being carried out in quite such a stupid way as it was in the UK, but everyone is clear that it's the public objection to immigrants that is the flashpoint.

How did you get that from the article? The agreements in place already allow immigration from eu countries, not a lot would have changed in this regard. The main problem is the further erosion of swiss direct democratic rights and sovereignty.

No, Brexit isn’t possible in Switzerland.

People voted for what is essentially Brexit, but the politicians refused to implement it.

https://en.m.wikipedia.org/wiki/2014_Swiss_immigration_initi...

Actually it is implemented as we speak, after years of tough negotiations, because that's the beauty of Swiss initiatives, they give the tone but not the legal terms - ensuring there's negotiation room, both internal and external. So depending on your personal definition it is succeeding or failing, but the fact is it is happening, there's no doubt about it. It's also not a "Brexit" because Switzerland never was part of the EU so using that name makes the discussion highly confusing for an outsider.

EDIT: I can’t add to my answer above but the point is to ask about how in the Swiss direct democracy model something as complicated as Brexit would have been handled (same? different?). I’m well aware Switzerland is not part of the EU. Apologies this wasn’t clear!

Switzerland would have to be part of the EU, for one.

Assuming the UK was using the Swiss model.

The Swiss negotiated for 7 years a general agreement with the EU (and failed at it in the end) so I would say no, the UK wasn't using the Swiss model.