The data network gets huge traffic due to iPhone usage
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.
But the total number affected by the outage was less than that because those with Blackberry handsets and on pre-pay tariffs were not affected, she added.
There were no problems with voice or text services.
O2 will also be the exclusive outlet for the Palm Pre, widely touted as the next credible threat to iPhone's stranglehold on the smartphone market,
which will create an additional large load of data network traffic
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."