After a second day in which hundreds of thousands of mobile phone users faced disruption, operator O2 is claiming it has now restored full service.

Thoughts now turn to compensation for those who have been unable to use send texts or make calls.

A message, or 'tweet' by O2 on social media website Twitter said: 'Our tests show that 2G and 3G services are now back for all affected customers. Let us know?'.

This came 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 and today 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 today 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.

Danny Edwards from Norwich emailed the Evening News and Eastern Daily Press office, saying: 'I am on 02 and have been for several years, I must admit this is the first time I have ever had a problem with 02.

'Yesterday afternoon my signal went for couple of hours, was unable to do anything with my phone apart from either turn it off or leave on the side as couldn't do anything with it. Around 5 o clock I regained signal and was able to re use everything on the phone. However at about 9.15 the signal went again and was unable to use my phone, I left my phone on charge over night and when I woke up this morning it was all back to normal again.

Many disgruntled customers took to Twitter this morning to vent their frustration at still being unable to use their phones.

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!!

Sean Foster (@SeanFoster) tweeted: 'Arrrrrrrghhhhh! My phone was fine all day yesterday and now after their failed overnight work o2 have screwed it!!'

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?'

Michael Allen, director of IT service management at technology performance company Compuware, said: 'In recent weeks we've seen how technology problems can have significant problems on the everyday lives of millions of people. First we saw the problems at NatWest and RBS and now 02. Not being able to make a call will be as serious to many people as not being able to take cash out of the bank.

'Unfortunately, these problems will only continue to increase unless organisations take a fundamentally different approach to the way they manage the performance of the IT systems we rely on to go about our day to day lives.

'O2's ability to deliver a service to customers will rely on hundreds of different components, systems and applications working in harmony. This can make preventing these types of service disruptions difficult as well as finding the root cause time consuming.'

O2, was formed in 2001, following the emerger from British Telecom of its former mobile business, BT Wireless.