@Persiantrio,
'Like you, I would point people to read LSE experts who have studied the impact of EU immigration to the UK since the A10 countries acceded EU membership. As you rightly say, J. Portes has much to say on the “lump of labour fallacy” in this regard. Also see extensive research by J. Wandsworth (2016, 2019). The 2016 report by Oxford Economics for the Migration Advisory Committee gives a very accessible explanation of why EU immigration was / is of net benefit to the U.K.'
The lump of labour fallacy is indeed a fallacy but, equally, if someone is prepared to do a job for a fraction of what it is 'worth' for a natal citizen as the GDP per capita is 1/3 of the GDP per capita in the UK in order to repatriate the money to an Eastern European Country, it will cost the jobs of domestic workers. I think that is fairly irrefutable.
'I can’t remember the exact stats, but it used to be the case that the vast majority of EU migrants settled in London / SE. These were migrants from “old member states” (France, Spain etc). What happened after 2004, was that gaps in the U.K. labour market (in construction, agriculture, processing) attracted migrants from new member states (mainly Eastern European) who were prepared to do jobs that U.K. workers simply were not. But the main change was the shift in settlement patterns. No longer contained in London / SE, they moved into more rural (and also culturally homogenous areas) such as Boston, Lincolnshire (the place with the highest Brexit vote).'
This is because the 'old' member states shared a roughly homogeneous economy with the UK and migration was driven by specific skills and opportunities in specific industries. These are too frequently found in London and the South East. More recent migration was arbitraging between minimum wage jobs in different economies with freedom of movement. Arguably, this is socially and economically destructive.
'But these areas have been depressed since the Thatcher era due to the failure of successive governments to invest. Immigrants did not “take your jobs.” If the immigrants has never come, the farms and processing factories would simply have closed - with far more devastating effects on the U.K. economy.'
That is arguable. You have no idea whether this would have been the case of not.
'There is no doubt whatsoever that EU immigration has been of net economic benefit to the U.K. This is fact.'
It is absolutely not 'fact'. And, even if it is probably true, it is very important to distinguish, as you did above, between migration from the 'old' EU of skilled labour, which was undoubtedly economically additive, to the migration from states with economies nothing like the rest of Europe, which was just displacing very low paid jobs as minimum wage arbitrage.
'Whether people in areas such as Boston didn’t like the fact that their high-streets were changing to include a few more Polish shops etc, is another matter. But feeling uncomfortable about change and economic fact are two very different things.'
Again you talk about economic 'fact'. These are not facts up to the standards of scientific proof. They are broadly believed economic truisms, which are impossible to prove or disprove (as economics, in this sense, is not a science)
To pivot from your expensive shopping on a Eurostar trip (from Waterloo) to a general argument about the pros and cons of Brexit does rather bring into question your rationale for posting.