just to pick up on a couple of other things…
“but seems quite sensitive about his accent (fretting that he never picked up a proper educated way of speaking), the school he went to, and even the fact that he wasn’t actually born in London but a small town somewhere north of there”
It is true that accent and dialect are a part of cultivating a respectable professional identity; it would be hard to be a barrister (say…) with a thick working-class Glaswegian accent. Working-class communities tend to have stronger regional accents and dialects (aristocrats, on the other hand, sound the same whether or not they come from Exeter or Edinburgh). Therefore, members of the working-classes are disadvantaged because of their speech patterns; in order to rise up the socio-economic ladder, they need to learn an ‘educated way of speaking’, which may well involve complicated and conflictual issues of cultural identity. Studies abound showing that working-class communities feel isolated and ostracised by the mainstream and ruling classes in no small part because their speech patterns are not valued or recognised.
Still, learning an accent is not an especially difficult thing. Most people do it naturally without even thinking about it. Fretting about never having learned an ‘educated way of speaking’? That’s weird. The standard ‘south-eastern’ middle class accent (with ‘bath’ pronounced ‘bahth’) is hardly the most challenging phonological nut to crack - Angelina Jolie managed it very well for Tomb Raider. I would go so far as to say that people don’t feel sensitive about their accents per se, they feel sensitive about their social origins, which are (or can be) manifested in their accents.
Secondly, the colleague in the OP felt sensitive about the school he went to. The vast, vast majority of children in the UK go to state schools, of which there is little to no publicly known ‘ranking’ of quality (well…there are actually league tables, but no-one knows the position of every school in them). I could tell you all that I went to Raynes Park High School in Merton, and no-one would be any the wiser as to what that implied about the quality of my schooling or my social class. OK, those who go to private schools in the UK are, quite understandably, classified as ‘rich’, and they tend to do better academically - but there is no stigma attached in going to a state school. I don’t understand how anyone could feel sensitive about ‘the school they went to’ in the UK, it doesn’t work like that.
University’s a bit different. There is a rough hierarchy which everyone sort-of knows - Oxbridge at the top, then the Russell Group, then the ‘okay’ universities, then the ex-polytechnics. When someone asks ‘which uni did you go to?’ they are, in a way, evaluating you based on your position in said hierarchy. But - and this is important - at undergraduate level British universities all cost the same*, regardless of how prestigious they are or the courses in question. You don’t need to be rich to go to Oxford, so it is not the elite preserve of the aristocratic classes. While universities like Oxford and Cambridge do have disproportionate numbers of ‘posh’ people compared to the population at large, they are no-where near as exclusive as some might suppose. Most people don’t get into Oxbridge because they’re not clever enough, not because they’re not rich enough.
(* okay, a bit more complicated than that…)
Thirdly, the guy was worried about the fact that he was not born in London. That’s the weirdest of all. Most people in the UK were not born in London. Most people in London were not born in London. There is no special privilege to having been born in the capital city - or certainly not that I am aware. That’s no to say that where you were born does not count at all in determining social status - but saying or thinking ‘I wasn’t born in London, therefore I am considered to be of less value’ is plain deluded.
All of this is a long-winded way of saying that the colleague described in the OP was talking bollocks.