I can’t describe it, but I know it when I hear it. Played with some kind of horn(s), and it starts out somewhat reminiscent of “The Girl I Left Behind” (the tune you hear when you see the ‘Spirit of 76’ painting).
I’m guessing you’re thinking of “Rule Britannia”?
The Sailor’s Hornpipe sounds quite similar to The Girl I Left Behind, but I’d describe it as more “nautical” than “regal”.
Nope, nope, and nope. Thanks, though.
British Grenadiers is close, but not it.
Ha! Shoulda done a little more research before posting. Rondeau by Jean-Joseph Mouret. Eh, that’s French, ain’t it? Oh, well.
“Pomp and Circumstance”?
That’s all right; back then, some of the British royals were French.
Over there, it’s “Land of Hope and Glory”.
It’s still “Pomp & Circumstance #1” to those who know their music.
Or, depending on your age range, “Macho Man Randy Savage’s entrance music”. 
Other frequently used ‘regal’ tunes:
William Walton : Crown Imperial
George Frideric Handel - The Arrival of the Queen of Sheba
Zadok the priest
Zadok the Preist?
ninja’dOh, I love Zadok the Priest, and found this flash mob version to be amusing.
Slightly abbreviated, but the looks on the faces of the people in the store are priceless.
“Anarchy in the UK” along with “God Save the Queen”?
Personally, I’d use “London Calling”.
Henry Purcell - Trumpet Tune & Air
Telemann, anything Telemann.
“I’m too sexy?” - YouTube
I am pretty sure it would be Zadok the priest.