Internal etymological reconstruction, as well as spelling, supports the connection of V with the vowel U in Latin, and comparative etymology shows that [v] in Latin corresponds to [w] in English. Phonetic considerations make it more plausible to suppose that the value [w] came first, and Latin [v] developed from [w].
These considerations don't tell us when [w] would have changed to [v] (except that English provides evidence that it happened after the split between the ancestors of English and Latin). So this isn't an argument for [w] being the value of V in "ancient Latin", just in some stage of the language that eventually developed to Latin.
The sound [u] is phonetically categorized as a "close back rounded vowel": "rounded" refers to the shape of the lips, which are brought together (there is a bit of variation between languages in the exact position of the lips). The sound [w] is pronounced mostly the same as [u], differing mainly in being non-syllabic. The sound [v] is further distinguished from [u] in several respects: 1) it is "labiodental", being pronounced with the lower lip against the upper teeth; 2) it has greater constriction than both [u] and [w], being categorized as a "fricative" consonant; 3) it lacks a "back" component.
Therefore, it is easier to explain alternation between [v] and [u] in Latin if we suppose that it was previously an alternation between [w] and [u], which are more similar to each other.