I was talking to an employee of my local health club, a normal bearded guy in his thirties, and I mentioned I was going to be away from home for a few weeks.
“Are you going on holiday?” he asked.
This suggested to me that the expression for Americans’ traditional “on vacation” has established a beachhead here and probably won’t go away.
notoneoffbritishisms.com 
Many decades ago it was common among journalists on national papers to say: “He’s touring in the west country” (Devon, Somerset and Cornwall) if someone didn’t want to be found by higher management, the publisher or outside authorities.
The band Green Day had a tune called “Holiday” more than a decade ago where the chorus ended with “on holiday”. Possibly been floating around for a bit, or possibly because it rhymed better.
Another word used by Brits is ‘jolidays’ (jolly holidays) or ‘jollies’, as in ‘I’m off on me jollies’, though holiday/s is most widely used.
As a side note, ‘jollies’ can also mean getting some sort of pleasure out of a thing, such as ‘he gets his jollies by seeing so-and-so doing such-and-such’.
The getting-pleasure “jollies” is also popular in the U.S. The first use cited by “Green’s Dictionary of Slang” (online) is Keith Waterhouse, “Soho,” 2002: “She would retire home after what she would call a day’s jollies […] at six p.m.”