When the Latin alphabet was first used in Old English, Latin w had already come to be pronounced v. The was no need for it in English at that stage, because v w

When the Latin alphabet was first used in Old English, Latin w had already come to be pronounced v. The was no need for it in English at that stage, because v was just considered a variant of f. But English made good use of w, and there were two ways of writing the w sound: either as two u's (because that way you can indicate the consonantalness of it, even before consonants as in writan) or using the old rune wynn. The uu approach spread to the continent and Old High German (which still used the English sound) adopted it. Old High German also didn't have a v sound at that time, and v was considered a variant of f - which it still is in modern German (e.g. Vater = father, pronounced fah-ta). Meanwhile, uu fell out of use in England, and the runic wynn dominated. But the English spelling system was gradually replaced following the Norman invasion, which led w to dominate over wynn. And v was now considered its own sound, so the letter began to be used for a v sound. So even though English seems to be a bit of a exception, with w=/w/, it's a practice that came from England and came back to England and was a medieval norm. But the w sound changed to v in German too. They didn't have such a radical interruption to their orthographic tradition as the English did, so the idea that V=F remained, and the letter w just come to be used for the new v sound. It spread from there. So it's not really w instead of v to distinguish /v/ from /u/. It's more w instead of v to distinguish /w/ from v=/f/. The crazy thing about that is it wasn't until several centuries after all that transpired that v and u became separate letters. So the Germans were using u for the sound of Buch and the sound of Uater (=Vater), and a different letter w for the sound of Wasser, when W and U=Buch were very similar and U=Buch and U=Vater were very different.