No, Tenet is not currently available on Amazon Prime UK. The most recent updates suggest that the movie will instead be released on digital rental platforms like Sky Store, Google Play Movies, Apple TV and YouTube. The movie will be available to rent on these platforms from as early as January 26th 2021.
In the meantime, if you are a UK fan of Christopher Nolan, many of his earlier films are available for streaming on Amazon Prime UK. These movies include; The Dark Knight trilogy, Dunkirk and Inception.
You can also enjoy other blockbuster titles on Amazon Prime UK, like Spider-Man: Far From Home, Sonic the Hedgehog, Deadpool, the entire Harry Potter movies, the Fast and Furious movies, plus many more.