The Hello singer's 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.
Tim Booth's band was leading sales at the beginning of the week (beg21Mar16), but Adele pipped the group to the post.
James' album debuts at two and Justin Bieber's Purpose drops to three in the new chart.
Jess Glynne's I Cry When I Laugh and Iggy Pop's 17th studio album Post Pop Depression round out the top five.
Meanwhile, Mike Posner's I Took A Pill In Ibiza has landed a second week at the top of the U.K. singles countdown.
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, rounds out the new top three.