Tea, sugar and coffee caddies - discolouring problem.

[Gizmonster]

I have a set of tea, sugar and coffee caddies, plastic coated - a nice deep red colour.
Well, the sugar ran out so I decided to clean it out. I soaked it in the washing up bowl (containing warm water and fairy washing up liquid) for a few minutes and then washed it out with a soft sponge. The problem is, it looks like the washing up liquid has reacted with the plastic coating, as it has gone all speckled and discoloured. I had this problem with the last set - yea too late now, but I remembered when I saw the mess.
I tried bleaching (nothing to lose as it already looks a mess), but that did nothing at all.
Anyone have any ideas how to restore it to its former glory ???