The most common and most likely answer to this crossword clue is the 4 plus 4 letter word NEXT DOOR
I've seen this crossword clue in The Sunday Telegraph
N
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More clues leading to the result NEXT DOOR
Buddy explains!

The straight part
We know that "very close!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very close! = next door.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 NEXT DOOR mean?
NEXT DOOR adverb- In an adjacent building, room or place.
- That occupies an adjacent place, especially the building immediately to the left or right.