I am having the exact same issue, started last night after midnight when I am playing World of Warcraft it just disconnects and I can't connect to some sites or back to Battle.net.
Of course there is not much point contacting VM as they will just deny all responsibility, seriously considering leaving and going back to BT. Never had a single issue with them for over 2 years, the 200mb(when I get it) is simply not worth it.
Same happening with me, 2 nights in a row I have disconnected from World of Warcraft then cant get on twitch or reddit but can use youtube and watch any video with no problems? The issue then fixes itself but may happen 3/4 times consecutively.