It seems that assuming there was no fog, visibility
actually was quite suitable and legal according to what you say. If I understand correctly, you were operating in a country where ATC and meteorological reports were not up to Western European standards and where the reported visibility was vastly worse than actual visibility.
Well I know what I would have done... But then I operate where more emphasis is placed on
actual weather and less on
reported weather. Not like the UK at all.
As an aside, calling "visual" and being told "continue" does not constitute a visual approach. I'd be looking for a phrase from ATC including the words "cleared" and "visual approach" before I made that assumption. But again I realise the ATC in that part of the world might not be so precise.