It seems his father was the driving force behind the obsession to make Alec an "Englishman", home-life revolved around his parents desire to be English above all else.Anglophile and not Greek are different things of course. That said Greek-British ties are even closer TTL than they were OTL...
Though initially Alec was baptized into the Greek Orthodox Church like his father (his mother's family being Roman Catholic), as he grew older his father decided that Protestantism was an important mark of being British and sent Alec to morning Sunday school every week. They attempted to observe the Greek custom of giving children lambs as pets which would then be slaughtered at Easter, Alec though opted to spare the lamb he was given that later grew into a big bad tempered ram (the idea of slaughtering lambs would forever put him off lamb chops).
In terms of language Constantine would always speak to Alec in English at home along with his young friends, Hulda would speak to him in German (later abandoning it in favour of English with an accent she never lost). Then there was the everyday language known as "kitchen" Greek which was used for communication with merchants, traders and servants, containing elements of not only Greek but like most pidgin languages was influenced by the vocabulary and grammar of the many different communities that used it (later in life he forgot anything other than English).
Alec's father was also the 2nd youngest of 8 children (two of which passed away in early in life), from the paternal family tree in the Official Biography it appears Constantine could have potentially lived for another two decades instead of passing away in 1923 (with the possibility Alec would not be an only child). With Constantine's older brothers likely having a greater role in the family business in Greece (and setting up shop in places like Beirut) it would be plausible for Alec Issigonis's family to decide to make the move to the UK in ATL (albeit in much better circumstances compared to OTL).
2019 numbers are of course skewed by heavy industry moving away to countries with relatively lower labour costs. Which is why Czechia or Slovakia or for that matter Turkey are producing more cars than Italy. That's why Sweden is a better model I think. If TTL Greece manages to be building half a million cars a year a century down the line I'd be more than happy. But that's far in the future. For all we know Greece by then may be third world with borders on the Olympus...
Guess ATL Greece being a major car producing nation depends on whether the defeated ATL Turks realise their revanchist ambitions or experience a similar fate as OTL post-WW2 Germany.