Both are correct!

Before the pound was decimalized, 12 pence were indeed a shilling, and 20 shillings a pound.

Of you go back far enough, I think it is true that at one time they were three currencies that floated against each other.

Huh? How does that work?

At risk of displaying my ignorance of English history, were they not at one time the currencies of three different kingdoms?

It's just like in fantasy novels, you have your silver and gold coins.

I always think of pence as 1/100 of a £, but pennies as multiple penny (1p) coins.

I’m not sure whether it’s just me.

No I agree that sums it up well - I can't think of a sentence that would sound natural (as in, sounds like a native BrE speaker said it) and have the same meaning with either one or the other.

Sounds like cents would be the American equivalent in that case.

Pence is the usual plural for an amount of money, although it's often replaced with "p" ("pee") when speaking informally.

Pennies means 1p coins, sometimes 2p coins too:

"Mum, I need sixty pence for the train, I've only got pennies and the machine doesn't take them."

"Pennies" without an amount means a small amount of money. "It's only pennies with the amount we use it."

(JK Rowling missed a trick. It should have been one bronze knut, two bronze knuts, and a price of four knets or something.)