Hi
Dying in a workhouse infirmary doesn't necessarily make a person a pauper. Many of these workhouses became hospitals with the start of the National Health system in 1946.
http://www.nhshistory.net/poor_law_infirmaries.htmTherefore the family may have claimed the body and chosen to have him buried in for instance the cemetery his wife was buried in (if she predeceased him) when the family were living somewhere else or indeed the local cemetery next door in Fulham/Hammersmith.
If the family didn't claim the body and he had a pauper funeral paid for by Fulham and Hammersmith poor law guardians, this unfortunately also doesn't guarantee a burial in the nearest cemetery. The cemeteries vied for workhouse business since they supplied a regular flow of 'clientele.' Consequently workhouses often went with the cheapest bidder and that could vary between cemeteries at different times. Westminster poor law burials for instance can be found in the large cemetery at Woking Surrey.
The guide which Dawn has already mentioned gives you a full list of London cemeteries in each area (with links) and the date that each opened. For a death in Fulham because you always have to start somehere I would start with Hammersmith and Fulham cemeteries. There are four listed managed by Hammersmith and Fulham, two of which were not open in 1886. Other than Brompton, which is an independently managed cemetery, the other cemeteries you list are not in Hammersmith and Fulham. If Hammersmith and Fulham fail to find him then Chelsea and Kensington managed cemeteries would be a logical next step, but not the first choice unless there is some further information that might suggest otherwise.
Hanwell - Westminster and Chelsea and Kensington
Gunnersbury - Chelsea and Kensington
Kensal Green independently managed in north Kensington
Hillingdon - Hillingdon
The guide
http://www.rootschat.com/forum/index.php/topic,403485.0.htmlThe two Hammersmith and Fulham cemeteries which were open in 1886 were Margravine (Old Hammersmith cemetery) already mentioned. It is on Margravine Road and Fulham cemetery (Old Fulham cemetery) which is on Fulham Palace Road.
Fulham workhouse became Fulham Hospital and now is Charing Cross Hospital as Jeannette has already stated
http://www.workhouses.org.uk/index.html?Fulham/Fulham.shtmlMargravine cemetery as she says is directly behind the hospital, Fulham cemetery is a bit further along the same road. Both are therefore equally strong possibilities.
Regards
Valda