Upon its release as a single, Radio Luxembourg DJ Mike Hollis, writing for the
Daily Mirror, stated, "Slade are back – and how! A tremendous single. I reckon the boys are set for a great 1984."
Tommy Vance, reviewing for
Kerrang!, praised it as a "good single" and added, "I know for a fact that this is based on a traditional tune or melody – I just can't remember which one. This is very cleverly done, however, and the sound is great." Bill Black of
Sounds noted the song was reminiscent of both
Big Country and
Thin Lizzy. He wrote, "Nobody's denying Slade their comeback, but on the backs of Big Country? Not quite. [They] take it one stage further and slip in amongst the '
Harvest Home' histrionics a passing reference to BC's biggest influence – Thin Lizzy circa '
Whiskey in the Jar'. Thus right in the middle of the song Slade slay us with a quick jig before launching back into the bagpipe guitars etc. So cheeky it's charming." 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." ==Chart performance==