I can only recall a few songs in my lifetime that was instrumentals that were hits. Apache by The Shadows The good the bad and the ugly from the same movie Ballade for Adeline - Richard Clayderman and lastly Crockett's Theme from Miami Vice. Also Kenny G was big in my days but then they started with using guest vocalists on their music.
Two big factors completely missing are 1) decline of Top 40 AM radio, and 2) decline of 7-inch 45 vinyl singles.
I remember the following instrumental hits of the era, they may not have reached number 1 but were definitely played a lot on air and were in my parent's (and then my) record collections. I'm sure there were many more.
Classical Gas - Mason Williams.
Telstar, Walk Don't Run, many more - the Ventures
Tequila - various
Midnight in Moscow - Kenny Ball
Work Song, Taste of Honey - Herb Alpert
A Walk in the Black Forest - Horst Jankowski
Alan Parsons - I Robot (FM radio)
Close to the Edit - Art of Noise
Music to Watch Girls By - Bob Crewe Generation
Let there Be Drums - Sandy Nelson
Topsy, Big Noise From Winnetka - Cozy Cole
Cast Your Fate to the Wind - Vince Guaraldi
Stranger on the Shore - Acker Bilk
Bonanza - Al Caiola
Like, Long Hair - Paul Revere and the Raiders
Theme from A Summer Place - Percy Faith Orchestra