Economists aren't exactly noted for their expertise in Cultural Studies (I think that's what I'm doing here), but I'm going to give it a go.
The fact that the Arthurian legend still resonates 1,500 years later tells us something about people, their hopes and fears. According to legend, Arthur was the British resistance leader who fought the invaders. His side eventually lost, which is why I am writing this post in English and not Cornish. And the Arthurian legend all begins with Vortigern's failed immigration policy. Vortigern invited some Saxons to settle in Brtain, and they invited other Saxons to join them. Which is why England exists. (It's ironic that the Arthurian legend is so popular among the descendants of his enemies.)
When economists disagree with public opinion, I normally agree with the economists. But we ought to think twice when this happens. Maybe, just maybe, public opinion is based not on ignorance but on something that our models leave out. When it comes to immigration policy, I think it is correct to say that elite opinion (which includes economists) in rich countries that are attractive to immigrants is generally more favourable to immigration than is public opinion. The elite finds public opinion a bit embarrassing, and tries to ignore it. They remind me of parents trying to get their kids to eat broccoli: "It's good for you, and you will like it once you get used to it".
The basic economics of immigration are quite simple. If we assume constant returns to scale, with output a function of labour and capital, and realise that increased labour creates increased capital (either immediately through capital inflows or slowly through immigrants' saving), everything expands in proportion. Both supply and demand for labour expand, leaving real wages, per capita income, and the unemployment rate, all unchanged.
If the central bank fails to increase the money supply and aggregate demand in line with increased aggregate supply of goods, it is true that immigration will cause a recession and increased unemployment. But then a stupid central bank will likely be equally stupid with or without immigration.
If we add land to the model it changes the results a bit, because land can't increase in proportion to population. So house prices (strictly the prices of building land) will rise. This hurts those natives who rent, but is a benefit to natives in aggregate, who get increased demand for the houses they own. Nobody forces them to sell or rent at higher prices.
If we add national debt to the model the natives benefit from immigration, because immigrants pay part of the burden.
There may be pros from non-rival goods (spreading the costs), and cons from common property resources (crowding).
There are lots of other potential pros and cons of immigration for the natives, depending on various details like whether the immigrants will be richer or poorer than the natives, and redistributive taxation, but that's the big picture in the standard model.
There may be economies of scale, but it is not obvious to me whether countries with larger populations are richer or poorer per capita than countries with smaller populations (though Malthusian and Tiebout effects would give reverse causation and make it difficult to interpret any correlation). And large cities can presumably capture the advantages of economies of scale in all but the smallest countries.
So immigration probably doesn't matter much for natives; but for immigrants it can sometimes matter a lot.
But if you explained that standard model to Arthur, I don't think it would change his mind about Vortigern's immigration policy.
And if you accused Arthur of being irrationally prejudiced or fearful of "The Other", I'm not sure how he would respond. Probably reach for Excalibur.
Maybe the standard model leaves something out? Starting with Arthur wanting to continue to live in Britain, and not England. People's preferences can be a bit conservative like that. Foreign holidays are OK for a bit of novelty, but it's nice to come home afterwards. Most people don't want to be forced to live in a "foreign" country.
What else might it leave out?
A sensible immigration policy would be careful to avoid the Vortigern mistake.
[Update: I am talking here mostly about legend, rather than what actually happened in post-Roman Britain. But I strongly recommend Razib Khan's "Celts to Anglo-Saxons" on the latter.]