The most common and most likely answer to this crossword clue is the 6 plus 6 letter word COVENT GARDEN
I've seen this crossword clue in The Guardian
C
O
V
E
N
T
G
A
R
D
E
N
Buddy explains!
The straight part
We know that "part of central London" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of central london = covent garden.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.