The network problems have affected more than O2 customers, hitting other services that rely on the data. It also said that the issue could be causing "intermittent problems" when customers make voice calls too.
The mobile network then followed their message up with: "Outage Update: One of our 3rd party suppliers has identified a software issue in their system". Our technical teams are investigating.
Calls are still working, O2 said.
"We'd encourage you to use Wi-Fi wherever you can and we are really sorry".
Moving photo of President Bush's dog paying tribute
On Sunday, Bush spokesman Jim McGrath posted a picture of Sully lying by Bush's flag-draped casket, which quickly went viral. Other Bush family members are expected to be at the Maryland military base for the arrival.
"We apologise for any inconvenience", the firm said, after problems were first reported at around 5.30am.
The mobile network said it had set up an urgent investigation after customers reported being able to get online or use mobile date from the early hours of Thursday. These include subsidiary Giff Gaff, and third-party networks, notably GiffGaff, Tesco Mobile, Sky Mobile and Lycamobile. GiffGaff has confirmed its service is also offline. The company estimated 32.1 million people use its mobile network in the UK. Londoners, for example, are finding that the Countdown timers at bus stops are all crippled as they can't communicate with London's transport executive, TfL.
Tens of millions of smartphone users in Britain lost internet access today after a software glitch brought down O2's data network. "This issue is being investigated". Our technical teams are working extremely hard to resolve this.
"Updates will be shared here as soon they are available".