I'm not sure of the current export situation but remember in the 60s the home market was absolutely massive in this country with very few foreign cars being sold here. And if we do produce more cars now, any profit goes to foreign companiesThe BL models built overseas were supplied with a lot of British built components so that would have entailed ferry van movements.
You're right about innocenti in Italy, they built minis and there own little hatchback also called mini which used mini engines and subframes, it predated the metro but unfortunately had less room than a standard mini.
They also briefly produced the allegro and called it the innocenti regent