The most common and most likely answer to this crossword clue is the 7 letter word EGOISTS
I've seen this crossword clue in Independent
E
G
O
I
S
T
S
More clues leading to the result EGOISTS
- Narcissists say it’s so messed up
- Self-absorbed characters in El Salvador find lead!
- Self-interested people say it’s so ridiculous
- Self-interested people say it’s so messed up
- Selfish people in English society progress first
- Tess and I go crazy for clever dicks!
- Say, nothing sits right with self-centered people
- Say love is nursing street people with swollen heads
Buddy explains!
The straight part
We know that "people with swollen heads" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case people with swollen heads = egoists.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.