I’m not sure I would call Kate Atkinson literary—but maybe I’m just being a snob because the stories are good, and there’s a feeling that a story that has plenty of popular appeal can’t truly be literary. I’ve read the three Jackson Brodie novels and have preordered the fourth. I thoroughly enjoy her writing in itself, rich with unsparing internal glimpses that sound as candid as unfiltered private thoughts in the characters’ minds (a trait I admire in George Eliot, too, having just freshly finished The Mill on the Floss, wondering, as I did so, how many people are left who can and will read Eliot for pleasure).
Andrea Barrett and Tobias Wolff are two contemporary writers whom I would call literary. They also tell good stories.