Spotify has rogue entities accessing its APIs. These folks see when you create an account and make false charges to your bank account thinking that you will not notice. They are not using banking information you provided to Spotify - they get it elsewhere. Spotify is fully aware of this but will not address it.
Sounds like a legitimate charge to me, £9.99 a month is the regular Premium subscription payment if you're subscribed directly with Spotify.
Since you're getting two Spotify charges, let's make sure you don't have multiple accounts following these steps. You might have two Premium accounts, one via iTunes and the other one through your card.
In case you only have one Spotify account, you can check what payment method it's using by loggin in here. If the account is set up with your card, you'll need to contact Apple for more information about the £12.99 payments.
Let me know what you find.
“Music acts like a magic key, to which the most tightly closed heart opens.” ― Maria Augusta von Trapp