She is on his mind because Alroy Kear, a fellow novelist, has asked him for help in writing a biography of Edward Driffield.  
This novel opens with the narrator slipping into a reverie about his childhood at Blackstable, where he first met the subject of his scholarship.  At the end of the novel, the narrator discovers that his former lover ran off with Lord George Kemp because he was a perfect gentleman.  She is on his mind because Alroy Kear, a fellow novelist, has asked him for help in writing a biography of Edward Driffield.  The "skeleton in the cupboard" of the subtitle is Rosie, Driffield's first wife.  FTP, identify this novel narrated by Willie Ashenden, a work of W. Somerset Maugham.
This novel opens with the narrator slipping into a reverie about his childhood at Blackstable, where he first met the subject of his scholarship.  
Cakes and Ale