This seems to be a useful guide if you are carrying ashes into the USA. Some of the rules may apply elsewhere.
Information issued by Australian Government Deaprtment of Health.
"There are no requirements for bringing human ashes into Australia or exporting ashes out of Australia. However, the container used to hold the ashes should be free from contaminants such as soil, and containers made from wood must be declared to Department of Agriculture and Water Resources (Agriculture) on arrival or before departure."
If you intend to bring human remains or ashes into or out of Australia, it may be helpful to contact a funeral director or a customs broker to assist you with the process.
Information from the UK Government
In today's highly mobile society, family members, relatives, and friends frequently live thousands of miles from each other. Despite this separation, people often desire the burial or scattering of their earthly remains in a location they consider significant, whether in their birthplace, where they went to school, a scenic spot, etc. While a licensed funeral director usually handles the shipment of human remains for burial elsewhere, an immediate family member generally assumes possession of a loved one's cremated remains or "ashes."