The complaints, filed in October through December, follow earlier lawsuits by Nokia claiming that a broad swath of Apple products violate its patents. Apple has earlier responded with its own infringement claims against Nokia.
The actions "add 13 further Nokia patents to the 24 already asserted against Apple in the U.S. International Trade Commission and the Delaware and Wisconsin Federal courts," the world's largest handset maker said Thursday.
In October 2009, Nokia filed its first patent infringement claim against Apple in Delaware.
Nokia spokesman Mark Durrant said he did not expect a quick result and that the first case likely would not go to court until late next year, probably in the Hague, Netherlands.
"We wanted to be sure that we don't just talk about these in dribs and drabs. There's obviously a lot of action going in some of these cases," Durrant said.
Apple representatives were not immediately available for comment.
Nokia's cases filed in the U.K. High Court on Dec. 3 include patents relating to touch user interface, on-device application stores and technology in signal noise suppression.
Nokia said at least two of the patents, including "using a wiping gesture on a touch screen to navigate content and enabling access to constantly changing services with an on-device app store," were filed more than 10 years before Apple's launch of the iPhone.
Nokia's share price was unchanged at €7.48 ($9.90) in late trading in Helsinki.