O2 said it believed it has restored full service to all customers as thoughts turned to compensation among the hundreds of thousands affected by the disruption.

O2 tweeted: "Our tests show that 2G and 3G services are now back for all affected customers. Let us know?", more than 24 hours after the network received the first reports of problems.

A spokesman said all users should restart their phones while those with smartphones who had turned off their 3G service could now reconnect. The company offered no further word on compensation after earlier saying that it was "focusing on getting full service resumed for all of our customers".

Engineers worked through the night to fix the fault with one of the network's systems which meant some mobile phone numbers were not registering correctly. They restored 2G access earlier and told customers with smartphones to turn off their 3G data to allow them to make calls and send text messages through the repaired network.

Many disgruntled customers took to Twitter to vent their frustration at still being unable to use their phones. Sean Foster (@SeanFoster) tweeted: "Arrrrrrrghhhhh! My phone was fine all day yesterday and now after their failed overnight work o2 have screwed it!!"

Another Twitter user Leanna May (@LeannaMai) said: "I can't bare this any longer!! THREE @o2 contracts, NONE WORK. And I'm at home pregnant in agony! Great, who should I call? No one!!" David de la Mere (@dmeeno) also took to the micro blogging site, tweeting: "I probably shouldn't have been so smug about having an @O2 signal yesterday. I don't have one now."

Tesco, which uses O2's masts for its Tesco Mobile network, confirmed that some of its customers were also affected. Consumer group Which? urged anyone who lost service to log any costs they incurred to claim compensation.

The watchdog's executive director Richard Lloyd said: "We want to see O2 offer compensation to all customers who have been hugely inconvenienced by this service blackout and have been paying for a service they cannot use. People should also keep a log of any costs they incur to help with any claims for compensation."

High profile users tweeting their frustration included BBC presenter Huw Edwards who wrote: "19 hours and counting #O2", while former Home Secretary Jacqui Smith tweeted that she had been unable to speak by phone on London radio station LBC.

Conservative MP Robert Halfron tweeted: "Very disappointed with @O2...#have O2 lost it?"

Have you been hit by O2 network failure?

Let us know if you have been hit by the O2 network failure by clicking the link below to e-mail us, or call newsdesk on 01633 777226.

Alternatively, via mobile on 80360 with the message ARGUS NEWS.

E-mail newsdesk