Nobody owns a dead body. (During Sheffield rag week many years , some students nicked a body from the morgue. They were only charged with stealing the shroud which covered the body, since there could be no ownership of the body). It follows that nobody owns the ashes resulting from the cremation of that body.
As stated above, the funeral director (or the crematorium) will give the ashes to whoever directly paid for the funeral. (i.e. the person who wrote the cheque, 'flashed the plastic' or handed over the cash). That person is free to do whatever he (or she) likes with the ashes.
Funeral directions, expressed in a will, have no legal standing whatsoever. (For example, someone could state that they wish to be cremated but whoever arranged the funeral would be free to substitute burial if that was their wish).
Chris