"To have cheek" or "to be cheeky" means that person is rude and insolent. A cheeky person asks for special treatment, but has done nothing to earn it.
Imagine a layabout who has stayed at his friend's place for three weeks, eating his friend's food and drinking his beer. The layabout doesn't clean, help or pay for anything. Then he asks his friend for money. The friend loses it:
"You have a bloody cheek, asking me for money!!"