My dad died recently his common law partner collected his ashes and has scattered them without telling me has she acted unlawfully

Yes. And I think that's wrong

At this point there is little you can do, it is not criminal but may have broken probate rules.

What was his wishes, where is this located, is there a will ( what was in it) if located in a place that allows common law marriage would that apply.

You may ( or may not) would have had a right to the ashes and probate could ( in my area) would tell you who, but they are gone and so really little can be done. If there was a urn, they may have to return it, if you were found to be the one with legal possession.

For the funeral home to turn them over to the partner it sounds like there was some legal right, or perhaps your dad had this preplanned with the funeral home.

Have you asked them why they turned them over to him ? Did he pay for the funeral ?

First ANY question on law needs to include your general locale as laws vary by area.

If she was his common law partner legally then she may have had legal rights. We also can't know what was presented to the funeral home or whether they were aware of the relationship or not.

So there are too many factors here to judge whether any laws were broken.