Lawyers for the Duke of Sussex notified the High Court that he would not continue the suit against Associated Newspapers.
Rooney accuses Vardy of leaking stories about her private life.
The High Court also refused an appeal following the Duchess of Sussex's legal victory.
Judge describes application as "fishing expedition" that risked "high-profile" identification of "innocent individuals".
The ruling has been described by charity Mermaids as a "devastating blow" to trans young people.
The group said allowing women to have medical abortions at home went against the 1967 Abortion Act, which was to prevent "backstreet" abortions.
Senior judges rejected their claims of bias.
Krzysztof Pokorowski did not receive reminders because he was sleeping on the streets.
A third of staff were set to walk out.
Hearing ruled the one-year-old had been sexually abused, but that this did not cause her death.