This is an odd single, an unknown group named Cliff White and the Dovers doing two non-hit Zombies songs “I Don’t Want to Know” (written by Chris White), backed with Rod Argent’s “Women”.
The group do a decent job on both songs, though neither cut has the magic of the originals. There’s a question of whether this is an English recording only released in the U.S., or if this is a U.S. act. I think the latter, as I found the English accent on “I Don’t Want to Know” to be contrived. Also, the production credit, M.J.B. Prod. for R.P.M. Ent. Inc. may give one clue, as RPM Enterprises was Charles Calello’s production company for some Lou Christie MGM recordings.
Released on 20th Century Fox 631 in the first half of 1966, the Mainstay Publishing credit is correct for the Zombies songs.
There was a Cliff White from London who was in a beat or R&B group in 1966, but went on to be a writer and reissue producer, but I don’t know if this is his recording. A suggestion that this was the Dovers on Miramar is laughable. 
The group’s name is likely to be a pun on the title of a 1941 song, (There’ll Be Bluebirds Over) The White Cliffs of Dover. The most famous version was by the English singer Vera Lynn (ironic, because there are no bluebirds in Britain), but Kate Smith had a hit with it in the US in 1942. Perhaps the parents of the guy who came up with the group’s name had a copy of the record in the house.