I'd forget about the cremation problem and concentrate on the probate one. If your husband hasn't got your sister's will, he needs to gain access to her house (or to get a trusted person to do so on his behalf) to search for it (or for evidence that it might, perhaps, be in the hands of a solicitor).
If a will is found, he needs to ensure that it gets into the hands of the executor(s). If he's an executor himself, he then needs to apply for a grant of probate.
If it appears that his sister died intestate, he needs to apply for letters of administration. (The process is basically the same anyway).
https://www.gov.uk/applying-for-probate/apply-for-probate
Returning to the cremation problem though, it might be worth contacting the crematoria in the relevant area to see if they can provide any relevant information.