Yes,it's a crime to remove stuff back out of public rubbish/litter bins,once you place something in one it becomes the property of the local authority or their contractor,its the same law as covers the removal of things from skips,even if you have "permissions" of the original owner,it's theft,you need to get consent from both the old owner and the owner of the skip,I had it all explained to me by a police solicitor when I was a regular skip diver,you removing an item permanently from someone else,who may have an income source for that item.
It even means you cannot remove even a bucket of soil from a skip full,even if the whole lot is going to landfill..