Cryptic crossword clue
W Churchill’s successor curtailed part of farmer’s livelihood 6

The most common and most likely answer to this crossword clue is the 6 letter word CATTLE

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The straight part
We know that "part of farmer’s livelihood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of farmer’s livelihood = cattle.
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.

What does CATTLE mean?

CATTLE noun
  1. Domesticated bovine animals (cows, bulls, steers etc).
  2. Certain other livestock, such as sheep, pigs or horses.
  3. People who resemble domesticated bovine animals in behavior or destiny.
  4. (English law, sometimes countable) chattel
  5. Used in restricted contexts to refer to the meat derived from cattle.

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