However, many have said that they are unable to make calls and texts also.
"The cause of today's network issue is in certain nodes in the core network resulting in network disturbances for a limited number of customers across the world, including in the UK", Ericsson UK and Ireland CEO, Marielle Lindgren, said in a statement.
The service status page of the O2 website added that "voice calls are working OK" and apologised for any inconvenience caused.
The outage is also causing other disruptions, such as issues with public transportation.
It said: "This allowed hundreds of people from both our technical teams and our third-party supplier's teams to focus on fixing the problem, helping us to restore data services as quickly as we can which will also help reduce the high network demand we're now seeing for voice calls".
Among them are busses, which uses mobile data to transmit timetable information to smart screens on London's network of bus stops, and taxis companies which use mobile apps to get custom and dispatch cars.
Huawei CFO's Arrest Could Hamper Commercial Ties Between The US And China
The Globe and Mail newspaper, citing law enforcement sources, said she is suspected of trying to evade USA trade curbs on Iran. Both countries have been locked into a trade war for much of the year, and only agreed last weekend to restart discussions.
O2 is the second largest mobile network in the United Kingdom, and supplies connectivity for other smaller networks including Sky, Tesco Mobile, Lycamobile, and GiffGaff.
"At 1.39pm on Thursday, December 6, 2018, the SoftBank Network Center detected software's malfunction in all of the packet switching machines manufactured by Ericsson, which are installed at the Tokyo Center and the Osaka Center, covering our mobile customers nationwide", SoftBank said.
"A review will be carried out with Ericsson to understand fully what happened", said O2, which is owned by Spain's Telefonica TEF.MC .
Thousands of O2 mobile phone users have reported problems using data and 4G services this morning. "Our technical teams are working extremely hard to resolve this", the company said.
"We'd encourage you to use Wi-Fi wherever you can and we are really sorry".