Furious customers of the network, which has a total of 32million customers and is the second largest mobile network in the UK, have taken to social media to flag problems with 4G and data services.
It appears that the network issues started about 5.30am, and customers across Manchester, London and Southampton have all reported outages.
But the issues have also spread beyond England to Scotland and Northern Ireland, a heat map by the Down Detector website shows.
The network, which is also used by customers with Tesco Mobile, GiffGaff, Sky Mobile and Lycamobile, is investigating the issue but has so far blamed it on a third party supplier.
A statement posted on the company's website read: "Our technical teams are investigating reports of issues when using data. Voice calls are working OK.
"We apologise for any inconvenience."
A statement on O2's social media commented: "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: o2.uk/ServiceStatus."
A spokesperson for O2 also told The Sun: "One of our third party suppliers has identified a global software issue in their system which has impacted us.
"We believe other mobile operators around the world are also affected.
"Our technical teams are working with their teams to ensure this is fixed as quickly as possible.
"We’d encourage our customers to use wifi wherever they can."
O2 has not yet given any estimate on when the issues will be resolved.
Apart from customers with O2, Tesco Mobile, GiffGaff, Sky Mobile and Lycamobile, the outage has also affected systems relying on the same network such as the electronic timetables for London's buses.