How about storing them coins? I'm not sure how things go about that in the UK, but most wallets I've seen on the US side of the world are made for cards and banknotes only.I wish the US would stop making $1 paper money.
I carry coins loose in my pocket, so I'd do the same for dollars (which is what I've done when traveling out of the US). It's a slightly different mindset, but people would get used to it. It's common to find coins from the 1970s in circulation but bills last only a few years.
The reason I ask is not only because I have my pockets busy with keys and the iPhone. I'm sure lots of people in the US are the same or similar. Making wallet space for coins will make them inevitably thicker, meaning less comfortable to wear and use. Just some thoughts out into the air.