The most common and most likely answer to this crossword clue is the 6 letter word ORATOR
I've seen this crossword clue in The Daily Telegraph
O
R
A
T
O
R
More clues leading to the result ORATOR
- Speaker from Dartmoor, a Tory
- Speaker setting out opposing sides of argument between two alternatives
- Speaker welcomed by senator, a Tory
- Chapel in the end excluding Yankee speaker
- Middle of statue gilded, it's suggested — Cicero, say?
- Speaker gets nothing right, a politician falling short
- Tory’s inside twice grabbing at the Speaker
- Rita the singer, model or public speaker
- “Speaker poor,” a Tory admits
- Alternatives include a third rate speaker
Buddy explains!

The straight part
We know that "Churchill, say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case churchill, say = orator.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 ORATOR mean?
ORATOR noun- Someone who orates or delivers an oration.
- A skilled and eloquent public speaker.