The most common and most likely answer to this crossword clue is the 7 plus 2 plus 5 letter word STRAITS OF DOVER
I've seen this crossword clue in The Guardian
S
T
R
A
I
T
S
O
F
D
O
V
E
R
Buddy explains!
The straight part
We know that "Our narrow separation from the EU" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case our narrow separation from the eu = straits of dover.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.