The most common and most likely answer to this crossword clue is the 7 plus 5 plus 3 letter word ENGLISH CIVIL WAR
I've seen this crossword clue in The Guardian
E
N
G
L
I
S
H
C
I
V
I
L
W
A
R
Buddy explains!
The straight part
We know that "Parliamentarians were on one side of this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parliamentarians were on one side of this = english civil war.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.