1. Yes, you do have rights! As owner of the yard, you can determine what is placed on your land. This includes your neighbour's bins. As you are the owner, you can remove any bins wrongly placed in your yard from the yard. Just because there might be a right of way over part of your yard in favour of your neighbour, this definitely does not give him the right to place his bins there. It makes no difference that this pathway might be fenced off from the rest of your yard. You can simply remove his bins and place them back on his land. If he disputes this, then you should get a solicitor to formally write to him and make clear you own this land and he has absolutely no right to place his bins there. This neighbour appears to be under a misapprehension that just because the area is fenced off from the rest of your yard that it is public property. AS it is not, you should make clear to him the position and remove his bins. If he persists, then get a solicitor to write to him.
Thanks very much for your help. There is no possibility that the pathway is land in common with all the cottages and that we all own the entire path?
2. Questions of land ownership are governed by the situation in the Land Registry. There is no magic to it. In your question you state that you have "check the land registry and we own this land and the alley way". So long as the Land Registry states "absolute ownership" then you own this land. There is no room for common ownership. The other cottages merely have a right of way over it. If there was common ownership your Land Registry would state co-ownership or tenants in common. So if you are unclear about this point check the Land Registry again. But if you own it, there is no room for common ownership.