I have tried Library of Congress online, WorldCat, Google, Google images of book covers (tip: these tend to never show the back cover), this website. So far, nothing.
Perhaps the words
SCIENCE FICTION FOR PEOPLE WHO DON'T LIKE SCIENCE FICTION
appeared in a display advertisement in a USA-based science fiction periodical. Perhaps the words appeared only on the back of the dust jacket or paperback. Book was a compilation, various authors collected.
Have already tried these variations: SF, SCI-FI, SCIENCE FICTION. DO NOT, DON'T. Nothing. Probably not a British book, but possible. Display advertisement never appeared in a UK science fiction periodical. Book probably from USA-based publisher. Possibly a mainstream publishing house, though this seems unlikely.
Book could be late 1960's.