Green’s Dictionary of Slang

cheek n.2

[the movement of the cheeks when speaking]
[mid-19C+]

1. verbal insolence.

2. audacity, impudence; esp. in phr. have the cheek (to), to dare, to have the nerve (to do something).

3. an audacious, forward person.

In derivatives

cheekiness (n.)

[mid-19C+] audacity, effrontery, impudence.

cheekish (adj.)

[mid-19C] impudent.

In phrases

to one’s own cheek [metonymic use of SE cheek, the side of the face]

[early 19C–1900s] to oneself, for one’s own private use.