Users complain that they can't access the internet on their phones as the network says it is doing all it can to fix the problem.
The problem is also affecting customers of Sky Mobile, Tesco Mobile, Lyca Mobile and GiffGaff - which all use O2's infrastructure.
The network said: "One of our 3rd party suppliers has identified a software issue in their system. Our technical teams are working extremely hard to resolve this. We'd encourage you to use Wi-Fi wherever you can and we are really sorry."
Customers tweeted that they were unable to use 3G and 4G services to access the internet.
Stacey Caine posted: ".@02 come on 02 unable to text anyone all my texts are failing, and no data. Currently using my WiFi."
Andrew Davies said: "Where has all the data gone.....@02 appears to have broken this morning! No mobile access on my phone Good job I have different provider on iPad!"
@anthony_vol1 posted: "Nice start to today 02 data has gone down, thank God for free Wifi on buses."
"Me, my mum and my sister don't have any mobile data either, we have 30gb showing on our 02 account!! Definitely think they have gone down," tweeted @stephanie_bint.
Nicola Barton said she was heading to Great Ormond Street Hospital when she realised data was down.
"Out all day at GOSH for appointments for my daughter and 02 decide today is the day for it's data service to go down. Fabulous, will rely on intermittent connections to wifi for the day then."
An O2 tweet added: "We are aware our customers are unable to use data this morning. Our technical teams are working on the issue with high priority.
"We are really sorry and working as hard and as fast as we can to fix this. Please keep an eye on our status checker: http://o2.uk/ServiceStatus ."
In London, the electronic timetables at the city's bus stops were also reported to be out of action - thought to be related to the O2 outage.