“Stephens, a media lawyer who previously represented Julian Assange, has told Newsweek the couple will be able to sue under the much more stringent British and European laws, even if a publisher is American.”
https://www.newsweek.com/prince-harry-meghan-markles-secret-weapon-protect-archie-paparazzi-revealed-media-lawyer-1498103

"They can sue in the U.K. if it's an online publication. They have privacy and defamation rights in the U.K. because they both have reputations here. The law is easier in the U.K. although, in California, privacy laws have become more stringent over recent years.”
“Only a handful of U.S. outlets would be exempt from European law. These include the New York Daily News which blocks access to their website from Europe. Any print or broadcast only coverage would also fall exclusively under US law, restricting the legal action available“