The song was written by lead vocalist Noddy Holder and bassist Jim Lea and produced by John Punter.

[8] "Run Runaway" was released on 7-inch and 12-inch vinyl by RCA Records in the UK, Ireland, across Europe, Australia, New Zealand and Japan.

On the CBS releases, "Don't Tame a Hurricane" appeared as the B-side, which would be included as an album track on Keep Your Hands Off My Power Supply.

Other sequences showed a marching bagpipe band and a kilted Scot (Ron Tarr) grappling with a caber.

[7] Upon its release as a single, Radio Luxembourg DJ Mike Hollis, writing for the Daily Mirror, stated, "Slade are back – and how!

"[12] Tommy Vance, reviewing for Kerrang!, praised it as a "good single" and wrote, "I know for a fact that this is based on a traditional tune or melody – I just can't remember which one.

"[13] In a retrospective review by AllMusic, Dave Thompson described "Run Runaway" as "storming" and wrote, "Building on the anthemic power of the earlier 'My Oh My', 'Run Runaway' is raucous chanting, swirling guitars, wild violin, and even a taste of heavy metal bagpipes, helped along by a drum sound that is pure early '80s.

The label soon repackaged The Amazing Kamikaze Syndrome into Keep Your Hands Off My Power Supply and released "Run Runaway" as the lead single in March 1984.