I actually don't even carry a nappy bag now that I have a caddy that fits everything and can go on my shoulder!
I love the Pram Caddy Shoulder Strap. It's exactly what I was looking for and makes my pram caddy alot more useful since I can also now easily use as a shoulder bag too. Makes day trips and getting things in and out of the car easier. Is durable and stylish. One comment is that the website photos make the strap colour look more cream, rather than light pink shade.