O2 UK chief executive Ronan Dunne told Sky News that "about a third of our customers were potentially impacted" its network outage.
That is roughly 7.6 million of the mobile service provider's 23 million customers.
He also said: "We absolutely want to make it up to our customers for the service that didn't get, the key for us now is to underpin the reliability of the service and restore our customers' confidence."
Thousands of disgruntled O2 customers took to Twitter this morning to vent their frustration at still being unable to use their phones.
Thousands of customers face a second day of disruption with O2's mobile network, despite reassurances that it has been partially restored.
Thousands of O2 customers across the country were still unable to use their mobile phones today.