uSwitch mobile phone expert Ernest Doku has advised users how to cope without data, saying: "O2 users affected by this mobile data outage will understandably be concerned and frustrated".
"Our technical teams are working with their teams to ensure this is fixed as quickly as possible".
The company is blaming software issues at one of its suppliers for the problems.
The company has confirmed that voice calls are still working, and have asked customer to alert them to any network issues they may be experiencing. "We'd encourage our customers to use wifi wherever they can and we apologise for the inconvenience caused".More news: Soyuz arrives at ISS on first manned mission since October failure
A statement on the O2 Twitter account reads: "We are aware our customers are unable to use data this morning". These include subsidiary Giff Gaff, and third-party networks, notably GiffGaff, Tesco Mobile, Sky Mobile and Lycamobile.
Transport for London's live bus timetables rely upon the O2 network. Transport for London said: "The company that updates the data to our network of Countdown Systems is now experiencing difficulties in providing this service".
O2 said it will be sharing updates on its website when the service changes. Our technical teams are working extremely hard to resolve this.
Many users took to Twitter to complain about the difficulties, which were first reported at about 05:30.