Harry, the younger son of King Charles, and six others including singer Elton John are suing Associated Newspapers (ANL) over alleged unlawful information gathering dating back 30 years.
ANL, which also publishes the Mail on Sunday and the MailOnline, has always denied any wrongdoing and previously described the claimants' allegations as "preposterous smears".
The claimants' lawyers had sought to amend their case to add a swathe of new allegations for the trial, which is due to begin early next year and could have Harry return to the witness box in his last remaining lawsuit against the UK press.
They argued last week that they should be allowed to rely on evidence that they said showed the Mail was involved in targeting Kate.
Her husband William is the heir to the throne and Harry's elder brother.
Judge Matthew Nicklin ruled however that the allegation that Kate was targeted by a private investigator on behalf of a Mail journalist was brought too late before trial.
In court filings, the claimants' legal team also made allegations for the first time that details about William's 21st birthday party in 2003 were obtained by "blagging" – obtaining confidential details about him by deception.
The claimants had not sought to add that allegation to their case and it was not ruled upon by the judge.
In separate litigation, lawyers have said William and Kate had their mobile phones hacked on behalf of journalists, and William privately settled a claim against Rupert Murdoch's newspaper arm.
ANL was also able to throw out some parts of the claimants' case, with Nicklin saying he would reject irrelevant allegations to stop the case "descending into an uncontrolled and wide-ranging investigation akin to a public inquiry".
But some of ANL's objections on the grounds the claimants were relying on findings from lawsuits against Murdoch's News Group Newspapers (NGN) and the publisher of the Daily Mirror were also refused by the judge.
A source familiar with the litigation said the claimants would seek permission to appeal against Friday's ruling.
ANL declined to comment.
