Used for someone you cannot get a straight answer out of. They dodge questions, wriggle out of promises, and somehow vanish the second money, favours, or responsibility comes up. It is basically calling someone a human escape artist, all polite and British on the surface, but definitely not a compliment.
"Did Gaz ever pay you back for that kebab? Nah, he’s slippery as an eel, starts chatting about the footy and suddenly he’s off down the pub"