The 27-year-old "Hello" singer's album 25 has edged out the band's new release Girl At The End Of The World to score a 12th non-consecutive week at number one, reported Contactmusic.
Tim Booth's band was leading sales at the beginning of the week, but Adele pipped the group to the post.
James' album debuts at two and Justin Bieber's Purpose dropped to three in the new chart.
Jess Glynne's I Cry When I Laugh and Iggy Pop's 17th studio album Post Pop Depression rounded out the top five.
Posner beat Sigala's collaboration with Imani and DJ Fresh, "Say You Do", to the top spot by just hundreds of copies, while Lukas Graham's former number one, "7 Years", rounded out the new top three.