According to <A HREF="https://en.wikipedia.org/wiki/Ralph_P._Boas_Jr.">Ralph Boas,</A> in his memoir <A HREF="https://books.google.nl/books?id=f-EWj5WtQHgC">Lion Hunting and Other Mathematical Pursuits</A> (page 10), it was not Littlewood but <A HREF="https://en.wikipedia.org/wiki/G._H._Hardy">G.H. Hardy</A> who asked these three questions to referees, as editor of the Journal of the London Mathematical Society. This is given as a first-hand recollection, so probably reliable:

<IMG SRC="https://ilorentz.org/beenakker/MO/Hardy.png"/>