OK so now their status reads:
"The network issue continues to be a top priority for us and we apologise to all our customers impacted by this.
Earlier today we suspended any planned works or updates across our systems and network. This allowed hundreds of people from both our technical teams and our third-party supplier’s teams to focus on fixing the problem, helping us to restore data services as quickly as we can which will also help reduce the high network demand we’re currently seeing for voice calls."
Hundreds of technical people? Doesn't smack of a software problem, or at least not a simple one. It sounds like a problem that requires a lot of manpower, like manually adjusting settings at thousands of different sites.
Today lots of things are going down for me and people I know, and we've actually had customers phone up and ask if it was due to the O2 problem!