you mention social mobility, but "social mobility" is only a concept that makes sense in a society based around class and sosio economic status, like is very typical in the UK, but less typical in other countries. So how can you compare like for like and make sense of any statistics. Compare to Norway, for example where you can barely get a foot into any workplace without further education and where you need certificates to be a waiter, and go through extensive sales and retail courses to work on shop floors, even though you are "just" selling clothes, but where the system is so flat that your salary as a shop assistant easily match that of a banker or a doctor. (almost)
After 20 years working his way up in the UK technology sector, and he still cant find a single company in Norway that wants to hire him, because he did not complete UNI. It is probably Just anecdotal, but it is happening.
I'm pretty sure the people who study social mobility across different countries have probably got it covered...
If Norway is anything like the country I am resident in (and I believe it is), education is free, Master's degrees are semi-expected for most professional roles simply because of that fact and because of the culture of most people who are at all academic usually studying that long, and vocational/training courses and certificates are a natural part of most jobs, however lowly.
Which means that unless you then try to introduce an (yet another) anecdote, specifically about an expat who did not grow up in the same culture and who is thus ill-equipped to compete in the market there, you absolutely can look at social mobility within the relatively closed system of country A and compare it with the social mobility within the relatively closed system of country B. And I find it very hard to believe the comment about a lowly shop worker earning near enough the same as a doctor, for example. That sounds like utter bollocks to me. I live in a similarly highly taxed country and the situation is absolutely nothing like that.
I'm honestly not sure what your argument is supposed to be re. the person (your DP? You don't seem to mention who it is unless I've missed it) moving to Norway. We were talking about social mobility within the UK compared to elsewhere. Not 'social mobility if a British person decides to go and try to slot into a country with a different education/work culture'. Really struggling to see how that is relevant.