O2 says technical teams are working "extremely hard to resolve this".
In a further tweet, O2 said the problem was related to a software issue in the system of a third party supplier. But data connections are broken.
The issue has affected an estimated 32 million people, as O2 also provides services for Sky, Tesco, Lycamobile, and Giffgaff mobile networks.
02 network suffers 4G outage
Some users have also reported problems with making voice calls, despite claims from O2 that voice services are unaffected.
Many users will have received an alert to their handsets warning of the drop in service.
O2 - which is the second-largest mobile network in the country behind EE - issued a statement saying: "We are aware our customers are unable to use data this morning". Our technical teams are investigating.
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US allies lobbied Pompeo to provide the 60-day window, hoping that a diplomatic solution can be secured during that time. Secretary of State Mike Pompeo also said that his country is suspending its obligations under the agreement.
"We apologise for any inconvenience", the firm said, after problems were first reported at around 5.30am.
That page was also having issues at the time of writing and was intermittently failing to load.
United Kingdom customers have reported not being able to use mobile data to access the internet and other services on the company's network.
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Police are continuing to investigate the disappearance of missing 22-year-old English tourist Grace Millane . The family have posted a plea on Facebook in the hope other travellers in New Zealand can help in the search.
The network outage has also affected Transport For London, which uses the O2 network for its electronic timetable displays at bus stops.
Nokia 8.1 is a global Android One phone with Pie
Luckily Chetan Cale, a gifted photographer and member of Nokia Community, was there to take some shots with it. Today the Nokia 8 .1 was revealed as a global phone, complete with an Android One version of Android Pie.