https://probatesearch.service.gov.uk/ has an index of probates. Not what you seek, but is relevant background.
I have found that site a bit tedious for that era.
But Ancestry.com has a similar record.
1992 probates
JAMES, Harold of 74 Main Rd Darnall Sheffield died 22 October 1991 Probate Leeds 22 January Not exceeding £125000 9281602172C

There are some family trees at Ancestry for this couple but none has the burial place.

https://www.familysearch.org/ark:/61903/3:1:3QS7-89F6-H9WJ-W?i=683&cat=444385
has an index of City Road cremations.
Image 684
1991
159019 James, Jane, age 83 years, July 5.
159868 James, Harold, age 87 years, Oct 28

You need to sign in to FamilySearch but it is free.

Many thanks for taking the time to consider the post Elaine. Jane Abdulla

Many thanks Terry, for giving your time to research this post it's much appreciated. It looks like they were cremated rather than buried. I'll take a look on family search too. Jane Abdulla

Hi Jane,

City Road Crematorium, Sheffield (Cremation INDEX) - Apr 4, 1905 to Dec 31, 1951 (*4)

As you can see our records of cremations only cover up to 1951.

Dont forget Bereavement Services at City Road.

Elaine.