The Dundee Michelin tyre plant closure (speculation about which circulated since even before the 2016 vote, incidentally) was put down to cheaper imports into Europe including the E.U. from Asia. So the idea that you have to be in the EU to be in manufacturing is clearly not the whole story here. Nor was it when car related manufacturing closed during the decades we were in the EU.
The wider story here is labour arbitrage. In or out of the E.U. it will continue to be.
As ever there's subtlety and complexity to any individual case. I'm no expert on Dundee but AIUI it shut in the first instance because the plant is out of date. There's then no appetite for renewal of investment because at least in part, as you say, the market is flooded by Asian imports. This is a result of competition combined with the extreme commodity nature of the tyre product, and the Asian product having reached the requisite level of quality, a comparatively recent development. You're also right in that this would almost certainly have happened with or without Brexit.
Manufacture of cars and a lot of component parts is a bit of a different story, for now at least. Firstly, mass manufacturing cars is hard, and there's a set of practical reasons associated with that as to why it continues to happen in fully developed economies rather than the cheapest sites globally. But less directly, it's also hard for new entrants to displace existing manufacturers, so there isn't disruptive competition as there is in Michelin's case. That pretty much means that if you're say, Ford, you're going to make roughly N number of cars come rain or shine and it's a choice as to where you locate to do that.
If you look at the patterns of automotive manufacture globally, it correlates very strongly with trade agreements. Suppose you buy a Fiat 500 in Europe. It's built in Poland in what started life as a Polski Fiat factory in the 1970s. If you buy one in North America, the same car is made in Mexico, which is otherwise a production oddity. The strongest reason for this is the economics of trade arrangements. So it is with most global car models (usually multiple manufacturing sites) where scale and conditions permit. Trump's tariff meddling and subsequent reorganisation is another good case study.
What's the point of all this? Well, whilst we continue to operate under capitalism & regional FTAs of some form, disruption to those trade agreements very likely mean jobs in that disrupted environment are at risk, more than from bog standard globalisation and all the usual threats. I think it would be dismissive & dishonest to say to UK automotive workers, 'hey it was already happening', because in the short to medium term at least, there very likely will be new negative consequences as a direct result.
That's an analysis as initially contained to the circumstances of one sector, rather than a universal property of Brexit, but there are similar examples elsewhere, like what remains of UK aerospace, and probably other STEM sectors.
Suprise surprise that hasn't happened.
