The most common and most likely answer to this crossword clue is the 11 plus 4 letter word STOCKBROKER BELT
I've seen this crossword clue in The Daily Telegraph
S
T
O
C
K
B
R
O
K
E
R
B
E
L
T
More clues leading to the result STOCKBROKER BELT
- Keep owing more, on strike in affluent area
- Farm animals changed direction, with rain starting to hit area just south of London
- Farm animals doing less well — a blow in expensive area
- Suburbia: standard stony fronts to regular buildings let in arrangement
- Devise block to berserk development finally in well-to-do area
- Prosperous area in Berks with bottle cork popping
- Goods train operator no longer fine, I hesitate to say, with speed in commuter area
- Maybe cattle dealer has fat controller when at home
Buddy explains!

The straight part
We know that "well-to-do area" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case well-to-do area = stockbroker belt.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.