If you take a glance at Golden Dagger and Edgar winners for that period you'll see that they overlap only once - when John Le Carré became the first of only two writers, both Brits as it happens, ever to scoop both awards for the same book. Of the other seven British Best Novel winners only two - Julian Symons's The Progress of a Crime and Eric Ambler's The Light of Day - secured a Gold Dagger nomination; the remaining ones didn't get any love and their Edgar success must have surprised a lot of people in their country of origin, probably including the authors themselves. Conversely, the Golden Dagger winners of the period barely made it to the Edgar shortlist, with only Lionel Davidson (The Night of Wenceslas) and H.R.F. Keating (The Perfect Murder) being able to achieve some recognition - but no win.
Obviously the Yanks had their own idea of what the best of British crime fiction was, an idea the persons concerned didn't agree with. The feeling was reciprocated for in the meantime the CWA rewarded two perennial American Edgar losers, Ross MacDonald and Emma Lathen, for books that the MWA had completely bypassed.
It was only the beginning. Over the next five decades both awards would routinely ignore each other's choices and now and then try to be smart by nominating/rewarding a book that was ignored on the other side of the Atlantic, a reminder that the Americans and the British still hold different views about "good" crime fiction - and that's fine by me. Besides, why should they agree when American awards themselves rarely do with each other? But more on this later.