The most common and most likely answer to this crossword clue is the 5 plus 5 plus 7 letter word GREEN WELLY BRIGADE
I've seen this crossword clue in The Guardian
G
R
E
E
N
W
E
L
L
Y
B
R
I
G
A
D
E
Buddy explains!
The straight part
We know that "privileged few going to the country?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case privileged few going to the country? = green welly brigade.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.