If they were Anglican, then it may be possible to find some details in the burial register for the parish in which they lived. They wouldn't have been buried in the churchyard by then, but if the funeral was held there, then the place of burial might. be noted (however, as a more recent register, this register may not be viewable anywhere)
By far the biggest cemetery in the area is Tower Hamlets Cemetery. It's certainly the closest https://en.wikipedia.org/wiki/Tower_Hamlets_Cemetery_Park
The records are in the London Metropolitan Archives , there are details about what they have and what indexes are available in the link below. . As you will see it's not that easy to search for a burial, especially if it is at all likely that it is a public one.
The leaflet also has details about other cemeteries; and of course in that period cremations are possible.https://www.cityoflondon.gov.uk/things-to-do/london-metropolitan-archives/visitor-information/Documents/05-cemetery-records.pdf
It may be that their family published the details of the funeral and burial in a local paper. I have the feeling though that this is probably less likely in the East End of London than a small town; but I don't really know.