Brady was convicted of the murders of John Kilbride (12), Lesley Ann Downey (10) and Edward Evans (17). Hindley was convicted of the murders of Lesley Ann Downey and Edward Evans.
The bodies of two other missing children - Keith Bennett (12) and Pauline Reade (16) - had not been found at the time of the trial. Brady and Hindley were strongly suspected of their murders. Pauline Reade was found in 1987 but Keith Bennett's body has still not been discovered. It is believed to be buried somewhere in the vast expense of the lonely, remote moorlands above Saddleworth.
Following Brady's death, the Coroner sought an "assurance" that Brady’s ashes were not to be scattered on Saddleworth Moor, where he buried his victims. The Coroner also wanted assurances that a funeral director and crematorium willing to take the Moors murderer’s body had been found - The Guardian 16th May 2017. The Coroner is reported to have said - "I also wanted to have assurance that when Mr Stewart-Brady is cremated his ashes will not be scattered on Saddleworth Moor. I have no means of making this an order but I think it is a right and proper moral judgement to make." It appears from a further report in The Guardian 17th May that the assurances were given to the Coroner by Mr Robin Makin who is Brady's solicitor and executor. The inquest now stands adjourned until 29th June.
Any will made by Brady has not been revealed and so it is not known whether Brady included any statements about what he wished to happen to his body. Wills normally become public documents following a grant of probate.
There is NO right of ownership in a dead body - Williams v Williams (1881) 20 Ch D 659. There is a common law duty to arrange for its proper disposal and this duty falls primarily on the personal representatives of the deceased - e.g. the deceased's executor if there is a will. The law was considered recently by Hayden J in the very different context of the body of an unburied child - see Gloucestershire County Council and Re K  EWHC 1083 (Fam).
What of the "assurances" referred to in the media reports? The Solicitors Regulation Authority (SRA) refers to "undertakings" which are defined in the SRA Handbook as:
" a statement, given orally or in writing, whether or not it includes the word "undertake" or "undertaking", made by or on behalf of you or your firm, in the course of practice, or by you outside the course of practice but as a solicitor .... to someone who reasonably places reliance on it, that you or your firm will do something or cause something to be done, or refrain from doing something."
Such an undertaking is a serious step for a solicitor to take since breach of the undertaking can result in professional sanctions. Undertakings are an important part of practice as a solicitor but they should never be lightly given.
BBC - 28th February 2000 - The Moors Murders