Elvis' first appearance on record here in the UK was "Heartbreak Hotel" in March 1956.

None of the Sun singles that preceded this in the USA appeared here at that time.

Here is the sequence that the Sun recordings FIRST APPEARED here (sometimes in oddball ways)

Important to note that RCA did not have its own label here until 1957 (distributed by UK Decca).

Previously all US RCA material appeared via EMI's HMV (His Masters Voice) label

Sun recorded titles appear in CAPITAL LETTERS

1956

Oct HMV CLP 1093 “ELVIS PRESLEY” (LP)
Blue Suede Shoes/I Got A Sweetie (sic)/I’m Counting On You/I’M LEFT YOU’RE RIGHT SHE’S GONE/THAT'S ALL RIGHT/Money Honey//MYSTERY TRAIN**/I’m Gonna Sit Down And Cry ((Over You)/TRYIN'TO GET TO YOU/One Sided Love Affair/Lawdy Miss Clawdy/Shake Rattle And Roll

It will be noted that Elvis' first LP here has a VERY DIFFERENT track lineup to the US issue. And although it has the same photo cover as in the US it has different home produced liner notes on the back (famously describing Elvis as "America's new JAZZ phenomenon"

Nov HMV POP272 BLUE MOON/I DON’T CARE IF THE SUN DON’T SHINE

1957

Feb HMV 7MC 42 Mystery Train/I Forgot To Remember To Forget (this was a special HMV release intended solely for export)

Mar HMV 305 BABY LET’S PLAY HOUSE/Rip It Up
Sep HMV 7EG8256 “GOOD ROCKIN’ TONIGHT” (EP)
BLUE MOON OF KENTUCKY/GOOD ROCKIN’ TONIGHT/MILK COW BLUES (sic)/JUST BECAUSE

Oct HMV 408 TRYIN’ TO GET TO YOU/Lawdy Miss Clawdy

1958
Oct RCA RB16069 “ELVIS’ GOLDEN RECORDS” (LP)
Hound Dog/I LOVE YOU BECAUSE/All Shook Up/Heartbreak Hotel/YOU’RE A HEARTBREAKER/Love Me/Too Much//Don’t Be Cruel/That’s When Your Heartaches Begin/I’LL NEVER LET YOU GO (LITTLE DARLIN’)/Love Me Tender/I FORGOT TO REMEMBER TO FORGET**/Any Way You Want Me/I Want You,I Need You,I Love You

** Although these tracks first appeared in UK in 1957 it was on a single INTENDED EXCLUSIVELY FOR EXPORT. The version marked ** is the first appearance on a regular UK-market intended issue

Other Sun tracks HARBOR LIGHTS,TOMORROW NIGHT,WHEN IT RAINS IT REALLY POURS make their first UK appearance on the same albums as they first appear on in the US (usually just a few weeks after US release)