The network went down yesterday lunchtime, leaving thousands of O2's 23 million customers struggling to make calls and send text messages.
According to an O2 spokesman, its 2G voice and data service has now been restored, while its 3G network will return gradually today.
O2 added that customers should turn their phones off and on again as the service returns.
Customers of GiffGaff and Tesco Mobile, which uses O2's infrastructure, are also understood to be suffering disruption.
The company has issued an apology on its site, claiming the service disruption is due to a system failure. It is directing customers to its "status reporter" tool, which allows users to check for disruption in their local area and responding to all customers on Twitter and Facebook.
O2 said in a statement: "We are sorry again for the inconvenience this has caused and can provide reassurance that we continue to deploy all possible resources and will do so until full service is restored."
In June O2’s network suffered a failure, with customers unable to send texts of a whole day. It comes ahead of the London 2012 Olympics, which is expected to put pressure on networks with the extra demand.
O2 is working towards becoming a "more conversational" brand and is overhauling its customer service.
It recently appointed Tribal DDB to rebuild its customer website, having admitted it was "confusing and frustrating".
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