For now there are a couple of YT videos arguing (usually) why Sheeran's song is not a case of infringement. Summaririzng them: the backing tracks sound similar indeed, the chords are not identic but close enough, the tempo is also close enough, while melodies are different. The videos point out that chord progressions can't be copyrighted.
In my analysis I will go beyond this level, and examine the plaintiff points in detail.The conclusion: this is not a case of infringement.
See similarity test results in the right menu.