News Group Newspapers (NGN), which has previously settled a large number of cases brought against the now-defunct News of the World, has always said there was no hacking activity at its sister tabloid.
But at a hearing in London today Mr Justice Mann allowed the claims to proceed.
The judge said four claimants could amend their cases to include the daily newspaper for the first time in the proceedings.
Two of those claims are among a number scheduled for a trial in July.
Up to 50 new claims against NGN, many of which will now include allegations of hacking at The Sun, are soon to be issued.
At the heart of NGN’s case is that the two publications were two different newspapers, which were separately run and did not share journalistic resources.
With the third round of the long-running litigation under way, about 1,000 claims have been settled so far – some within a compensation arbitration scheme set up by the group.
One of the new claims – which includes The Sun and which the judge refused to strike out – has been brought by Simon Clegg, the former chief executive of the British Olympic Association.
Others now suing NGN include EastEnders actors Christopher Parker and Brooke Kinsella, Coronation Street actor Kym Marsh, designer Pearl Lowe and her musician husband Danny Goffey and Leslie Heseltine, who is better known as actor and comedian Les Dennis.