LulzSec, which was thought to have disbanded at the end of June, began tweeting about the operation late on Monday night UK time. Its first act was to redirect The Sun's visitors to a fake news story claiming that News Corporation founder Rupert Murdoch had been found dead in his garden.
"We have owned Sun/News of the World - that story is simply phase 1 - expect the lulz to flow in coming days," a LulzSec representative tweeted.
"Within 30 minutes, pages are overloading, things are crashing! We are working our way through the cracks right now. Stay tuned for more," they later added.
LulzSec later wrote: "This was the work of Lulz Security, dear media. We would like to give a shout-out to our bros at @AnonymousIRC though, we love those guys!"
The organisation also retweeted selected messages containing personal contact details of News International staff. The tweets appear to be from members of Anonymous.
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LulzSec later redirected thesun.co.uk to point to their Twitter feed and proclaimed "We have joy, we have fun, we have messed up Murdoch's Sun", referencing the 1974 song 'Seasons in the Sun' by Terry Jacks.
By 1am UK time, The Sun, The Times and News International's corporate websites were all reporting 404 errors, although News Corporation's website appears to be unaffected.
James Ball, a data journalist for The Guardian, observed that News International's DNS servers and all their web addresses - totalling over 1,000 domains - are down.
Access to both The Sun and The Times's websites has now been restored.
More on News International and the News of the World phone hacking allegations:
> News of the World whistle-blower Sean Hoare found dead
> Jude Law sues News International for phone hacking
> News Corporation beefs up hacking cleanup committee
> Jeremy Clarkson reveals Rebekah Brooks, David Cameron Christmas party
> Rupert Murdoch's Wall Street Journal hits back over hacking scandal
Watch a clip from Sky News breaking news of the hacking - in which LulzSec is erroneously referred to as 'the Louise boat' - below: