Some users have also reported problems with making voice calls, despite claims from O2 that voice services are unaffected.
Calls are still working, O2 said.
In total, around 32 million customers are affected.
But now message from O2 is I've no internet connection.
In addition, London Bus timetables rely on O2's coverage, meaning that these were also down this morning.
O2 issued the following statement on its website: "Our technical teams are investigating reports of issues when using data".
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O2's data network is down across the United Kingdom this morning, the mobile operator said.
It doesn't end there, because some major MVNO (virtual networks) that piggyback O2 signals are experiencing the same disruption.
O2 says it is trying to resolve the issue as fast as possible. Woke up this morning with no mobile data at all and I have turned mobile data off and also powered my device down and still no mobile data?
Lewis Clinton said the problem is affecting many in the south west.
It was confirmed by O2 earlier today that the it has been identified as a software issue within the system of one of their 3rd party suppliers. We believe other mobile operators around the world are also affected. "We'd encourage our customers to use wifi wherever they can and we apologise for the inconvenience caused".
"Updates will be shared here as soon they are available".