The technology giant has apologised for the failure and detailed a compensation package for customers.
The firm said: "We’re very sorry about Thursday’s data issue. We understand how important it is to stay connected, especially at this time of year.
"We’d once again like to thank our customers for their patience. We’re doing all we can to make sure this issue doesn’t happen again."
The compensation packages are;
For pay monthly customers, SMB business customers and mobile broadband customers O2 will be crediting two days of monthly airtime subscription charges by the end of January.
For Pay As You Go customers O2 will be giving a 10% credit on a top-up in the New Year and O2 will let customers know when it is available.
For Pay As You Go mobile broadband customers O2 will be giving a 10% discount on a Bolt On purchase in the New Year and will let customers know when it is available
However this could work out as less than Â£1 as for those on the lowest tariffs paying Â£13 a month it would work out at 42p a day, or 84p in total.
If you are still not satisfied you may be able to leave your contract with O2. Ofcom states that in cases where you have been without service for some time, you may also have the right to leave the contract without penalty. There may be a term in your contract saying you can do this if your provider has failed in its obligations to you or breached a key condition.
Ofcom says that customers must follow the official complaints process first though, which is online here.