A spokesman for the mobile network, which has more than 22 million customers, said it was investigating the failure and aimed to fix it as soon as possible.
The firm did not identify the cause but it affects outgoing messages, with customers receiving "network out of order" messages from O2 when they press send. The firm believes it affects a percentage of pay monthly, but not pay-as-you-go, customers.
O2 could not say how many customers had been affected but insisted it had received relatively few complaints. A spokesman said the fault struck on Tuesday, but was "utterly confident it's not a 'significant problem' kind of number [of customers]".
Frustrated customers contacted O2 via its Twitter account.
Wendy Boland, a TV industry worker, complained that she was unable to reply to birthday messages.
Bradley Singer, an IT manager from North London, said O2's call centre staff were unable to say when the glitch would b resolved.
Last year O2 customers in the South East suffered major disruption when thieves stole vital equipment from a company data centre.
A spokesman for O2 said, "A small number of pay monthly customers – a few thousand – are currently experiencing difficulty sending and receiving text messages. Our engineers are working on the problem and expect to have resolved it later today. We apologise for the inconvenience this causes."
