There's not much point in looking for reasons in the first few minutes of an outage, as it's often caused by transient problems, so just sit tight and I'll update this post once it's back up, or I know what the score is.
UPDATE 14:14: Could be something a bit icky, as our host's sites are also affected. That sounds more like an internet issue that's preventing "us" getting to the server on which we're hosted, which probably means we'll need to be patient. If something pops up later, I'll let you know.
RESOLUTION: It was a problem with the UPS, which somehow tripped their switches, leaving a big bunch of servers without power. It took a little while to get access to reset them, but they managed to get it up & running again in a couple of hours.