The most common and most likely answer to this crossword clue is the 5 plus 10 letter word HOTEL PROPRIETOR
I've seen this crossword clue in Financial Times
H
O
T
E
L
P
R
O
P
R
I
E
T
O
R
Buddy explains!
The straight part
We know that "Basil Fawlty, say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case basil fawlty, say = hotel proprietor.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.