Solid coloured wallpaper for Home Screen on my iPhone
I'm assuming you are selecting from the official backgrounds that are under Settings > Wallpaper > Choose a New Wallpaper menu. There used to be more plain backgrounds available, but Apple keeps removing the older ones after each iOS update. If you want to access older iOS wallpapers, check out this gallery (there are some plain backgrounds under iOS 7):


iOS Wallpapers


In case you want to set your own wallpaper, simply save the image to your gallery, tap the share icon on the bottom left, and select the Use as Wallpaper option.