"Anglicized" is probably not the best way to think about it. The Latin letter "v" was pronounced "w" through the classical period, but had shifted to β or v (fricative) by the third century, long before English existed. V was pronounced v (voiced labiodental fricative) for many centuries. And though we do tend to give the classical period a lot of prestige, it was just one phase for Latin.
Funny part is, the same shift happened in a lot of languages. I think some more obvious examples are modern German and Polish, where letter W corresponds to the V sound. Although I believe that the shift happened in German and then Polish borrowed the letter with the new pronunciation.