I believe that Germanic always had the sound for which we use a “w”. The rune wynn/wēn was used for this sound. When the Anglo-Saxons started to use the Latin alphabet the wynn/wēn letter “Ƿ” was incorporated for the “w” sound, although there were variations in the north such as uu. When the Normans came they avoided using Ƿ and switched to u, v and uu instead. The letter finally settled on being w.
In other Germanic languages there was a tendancy for the sound to evolve from our “w” to our “v”. I think that the change was probably taking place during Anglo-Saxon times. I do not know why languages change but it seems to be a universal phenomenon, and particularly quickly in the Germanic languages. I am just reading where the Germanic “ai” changed to “ā” in old English, as in stone, but tended to change to “ei” or “ē” in other languages. Then the Germanic “au” changed to “ēa” in old English, as opposed to not changing or changing to “ou” or “ō” in other Germanic languages. Then you get the palatisation of “c”, “g” and “sc”.