O2 not working: Why is 4G and data is down on giffgaff and Tesco's networks?

O2's network has stopped working, leaving its customers unable to get on the internet. And its customers are feeling largely hopeless. The issues apply not only to O2 customers but to people on GiffGaff and Tesco Mobile, too. The cause of the problems is still largely mysterious. O2 said that it is aware of them, is working on a fix, and has suggested they are related to problems at a third-party supplier that have affected other networks around the world, too.