An O2 spokesperson confirmed the problems, saying: "Our technical teams are investigating reports of issues when using data".
The problems mean that the companies that share its network - such as GiffGaff, Sky Mobile and Tesco Mobile - are also being hit by the problems.
Some users are still reporting issues with voice calls.
In a tweet, the network said that the issue lay with one of its third-party suppliers, and recommended that users switch to Wi-Fi wherever possible.More news: XFL announces eight teams, cities and stadiums for its return in 2020
O2 said its technical teams are working with its supplier's teams to fix the problem.
Calls are still working, O2 said.
As a result users have been experiencing issues with 3G and 4G services, with others unable to make calls or send texts.
Customers of O2, GiffGaff and virtual operators who use Telefonica's network in the United Kingdom have been hit by a spectacular outage across the country.More news: Patriots QB Brady finally joins 1000-yard rushing club
In addition, London Bus timetables rely on O2's coverage, meaning that these were also down this morning. The company estimated 32.1 million people use its mobile network in the UK.
O2 says it is trying to resolve the issue as fast as possible. "We'd encourage our customers to use wifi wherever they can and we apologise for the inconvenience caused".
Thousands of customers are believed to have been affected in the data blackout, which is also affecting customers of other mobile providers who use O2's service. Our technical teams are investigating.More news: Sandra Oh and Andy Samberg to host Golden Globe ceremony