The most common and most likely answer to this crossword clue is the 5 letter word ACTON
I've seen this crossword clue in Independent
A
C
T
O
N
More clues leading to the result ACTON
- Continue to play a part in area of London
- Suit Italian leader abandoned for old jacket
- One leaves Battle for part of London on the tube
- Current fashion in something stuffed beneath mail?
- Continue to play in London
- … playing after do, somewhere in London
- Bill joins fashionable society somewhere in London
- Performance taking place in West London district
- Hundred added to bill in London district
- Tax cut oddly reduced working in London area
Buddy explains!

The straight part
We know that "London district" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case london district = acton.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.