Procol Harum hit #1 in the UK with “A Whiter Shade of Pale,” though only #5 in the US.
I’m not nearly as familiar with the UK charts, so there probably are other surprising examples as well. I do know that for most of the early 1960s in the UK, singles were left off of albums, on the theory that people didn’t want to buy the same music twice. That had to have some effect on singles sales, but it could go either way. People might buy more of the single because it was their only chance or they could buy fewer because hearing it on other peoples’ albums didn’t happen.
Anybody from the UK who can address this?
I don’t think The Knack had a single before “My Sharona”.
Kesha’s first release was an uncredited appearance in Flo Rida’s #1 single “Right Round,” and then she hit #1 again with her own debut single “TiK ToK.”
Along similar lines in the UK, Frankie Goes To Hollywood went:
Relax - #1
Two Tribes - #1
The Power Of Love - #1
Welcome To The Pleasure Dome - #2 (Awwwww…)
j
Fellow Liverpudlians Gerry and the Pacemakers had already debuted with 3 number 1s and then a number 2 in 1963/4.
In January of 1983 Men At Work simultaneously hit #1 with their first single (Down Under) and their first album (Business As Usual) in not just the US but also in Australia, New Zealand and the UK.
Heh. Per wiki, Gary Lewis & the Playboys got their #1 debut the old-fashioned way: “Garrett got airplay in New York City for “This Diamond Ring” by making a deal with WINS disc jockey “Murray the K” Kaufman, who ran a series of all-star concerts at theaters around the New York area. Garrett promised that if Kaufman played Lewis’ record, the Playboys would do his shows. Garrett then had Jerry Lewis use his contacts to get his son onto The Ed Sullivan Show.”
It was more than just theory. Record buyers had less money in the UK and did not like to waste it. So the three formats – singles, LPs, and EPs (which never caught on in the US) avoided repeating songs. Putting a song on more than one was considered a rip off.
I came in to mention these two. Then I found out it wasn’t Macklemore’s first single, which I honestly didn’t know.
Cyndi Lauper hit #1 with “Girls Just Wanna Have Fun,” her first single.
There were also unwritten laws that US pop albums consisted of 12 songs and UK albums of 14 songs. That’s why the early Beatles’ LP output (and that of the Rolling Stones and countless others) was so different in both countries.
Another from the U.K., Thunderclap Newman hit #1 with “Something in the Air” in 1969.
That isn’t true at all. In the USA, the first single was I Want to Hold Your Hand.
Love Me Do was the first UK single and not a number one, that was Please Please Me.
Ninja’d
A-ha’s Take on Me was their debut song and reached #1 on the US charts. Might be a bit of a cheat though, they released a second version of the song after the first failed to chart; but it was still the same song.
Men at Work probably qualify, depending on how stringently you want to define “first single.”
They had been around for a couple of years, working as a “pub band” in Australia, and then signed their first record contract, with CBS Records, in early '81. Their first single once they had that contract, “Who Can It Be Now?”, reached #1 on the U.S. Billboard chart.
However, prior to signing a record conract, they had self-released at least one single in Australia – a song called “Keypunch Operator,” which apparently did not chart in Australia (or anywhere else, for that matter). The B-side of that single was an early version of “Down Under” – a re-recorded version of that song was their second release with CBS, and it, too, reached #1 in the U.S.
Edit: I didn’t see that Snowboarder Bo had already mentioned them – sorry!
“If You Had My Love” looks to qualify as a debut #1 for Jennifer Lopez.
Also their only #1 from their only album. I had fun playing bass on the album. 
I guess it’s time to mention the one-hit wonder that was Zager and Evans, with the truly weird #1 debut that was In The Year 2525.
Yes! I was hoping you might see your group namechecked and drop by! 