Not all vines suffer from mildew, but some, such as the very popular Black Hamburg, are very vulnerable. Rather than wondering why the mildew has spread what you need to understand are the conditions in which mildew can flourish, such as a damp atmosphere and poor growing conditions. Unless you want to drench all your plants with fungicides, which I would not recommend, and might not be fully effective, you should look at cultural conditions.
Later in the season and especially when there are low light levels and high humidity, it is difficult to keep plants free of this disease.
In our polytunnel, for example, although the tomatoes and peppers remain fine, the courgette plant is affected and soon I know this will spread.
My advice is that you should replace your vine with a resistant variety, or grow one outside instead, and then your other plants will be less likely to be affected if you keep them healthy and don't allow humidity to build up.