Hello, Paul,
I have always understood that a burial could not take place without a death cert.
I had wondered whether Alfred had been a second given name & he had dropped the first name, but of all the Rush lookups found none with an Aflred for first or second. I also thought about a war death, but could not think, off hand, of any conflict taking place 1857-'61. The Crimean war ended in 1856, I suppose he could have been a casualty who died later but there should be a record somewhere for him.
I have searched the National Burial Index but there was nothing for him in any county.
I had been looking for Alfred in Rutland, not found anything useful so broadened the search for all counties but only found there were several Alfred's in Suffolk, but how to tell who was the right one, I just don't know.
Sorry to be at a deadend on Alfred.
Meliora