It was an official release. Carrie referred to it as such; Sony shortened it, by reducing the intro and one of the later instrumental passage (although, in my opinion, those were pretty integral to the track); and the BBC added it to their radio playlist, from which DJs and producers select songs to put on air, in joint consultation. In any time frame, Radio 2 have playlists of varying importance - unfortunately, "Chaser" wasn't put on the A List, which probably reduced its chances of getting much general music rotation. As far as I know, it didn't attract much attention.
Carrie (like other Country artists) is mainly seen here as an album artist., and singles have nothing like the heavy promotion they still receive in the US. "Storyteller" did well, reaching no 1 in Country Albums and no 13 on the General Album chart. (It was also nominated for International Album of the Year at the BCMA, along with "Smoke Break" for International Song - but lost out to Chris Stapleton)
As far as I know, her only single to feature in the Official UK charts was "I Know You Won't" which reached no 94 in the top 100 in October 2014. (I don't know if anyone wants to consider that as a 6th single, as it was well after the Carnival Ride era in the US. )
Carrie Underwood | full Official Chart History | Official Charts Company
SH and CR were belatedly released together in this country, as Carrie became better known. "I Know You Won't" was released as a single even later, by RCA - another label within the Sony stable - presumably to coincide with publicity Carrie was getting.
Apologies to those who disagree - but, in my opinion "I Know You Won't" was, by several orders of magnitude, a superior song to LN or AAG. It was one of three standout songs on CR co-written by British songwriter Steve McEwen, along with JAD and GOTT - (he also contributed one that didn't quite match those three, TMBIM - but we'll let him have that one. The song suits Carrie's feisty delivery, and as lighter fun songs go, I still prefer it to the two that were singles - just not by several orders of magnitude)