"Our technical teams are working with their teams to ensure this is fixed as quickly as possible".
Down Detector shows a sharp rise in customers reporting outages since around 0445 GMT today.
O2 said that "one of our third party suppliers has identified a global software issue in their system". Voice calls are working OK.
An O2 spokesperson said the network was continuing to investigate the problems.
"We apologise for any inconvenience", the firm said, after problems were first reported at around 5.30am.
CUSTOMERS WHO rely on the O2 mobile network are waking up to a whole crock of bork this morning, as a major outage affects customers on the United Kingdom number two provider and its dependencies.
O2 has 32 million customers, including people signed up to Tesco Mobile, Sky, Lycamobile and GiffGaff. It also affected services that use O2's network, bringing down digital timetables at London bus stops... "This issue is being investigated".
"We'd encourage you to use Wi-Fi wherever you can and we are really sorry".
Some customers have reported being unable to use their data, while others are struggling to send texts.
The company, the second-largest mobile network in the United Kingdom, said it was investigating the technical fault.
O2 said it would share further updates as soon as they were available.
Some customers can not even reach the service status page.