The “vast majority” of O2 customers who lost internet connections on their mobile phones have had their service restored, a company spokesperson said.
The network outage left hundreds of thousands of UK monthly contract users without access to the web or multimedia messaging from Tuesday afternoon.
O2 said the problem was with the allocation of internet addresses that permit a data network connection.
The company holds an exclusive contract for Apple’s iPhone.
More than two million of O2’s 20.8 million customers use its data services, an O2 spokesperson told the BBC.
In a statement, the firm apologised for the outage, saying “We have managed to restore data services to the vast majority of customers and are doing everything we can to ensure the few remaining customers are back online as soon as possible.”