Well, everything is bit slow for me. I'm in the UK on Virgin Media, using either Google DNS or the VM ones (I'm not sure and can't be bothered to look).

What has just happened, and it can't be coincidence, is that I lost internet connectivity about 1 hour ago, and had to reboot my Cable Modem to get it back.

I'm fairly certain that my ISP was affected by this causing an outage of all internet traffic for my network. So it seems possible, although I imagine using an alternate DNS provider should work ok (if they're not overrun by extra traffic)?

Unfortunately I'm not sure what the default DNS on the modem points to..

You can try https://dnsleaktest.com/ which shows which DNS server is actually used.

I read it brought down the Vodafone network in Czechia, one of the major providers there.