Coins? Haven’t seen anything with a coin part that could be described as “slim”. I just keep some in a little bag in the car for parking.
I got an Aspinal wallet via their ebay store (they sell off embossed initials ones cheap), and have ended up just using the removable ID part of it (like this).
Clear side has my driving licence and a credit card to beep in/out on London transport. Other cards go in the other side, with a few notes tucked in the part behind those.