English/Welsh death certificates don’t provide any details of burial.
The Shoreditch Infirmary became St Leonard’s Hospital, and the records are therefore classed as hospital records, not as poor-law records. They are not part of the Shoreditch Board of Guardians records at this date.
They are at London Metropolitan Archives (not the National Archives). They are not online.
There are no admission or patient/clinical registers for 1918. The only register for that period is the Register of Deaths, Feb 1884 – Oct 1940, H19/SL/B/03/001. This may or may not refer to burial.
Clearly you have some reason to believe he died in the Infirmary? If you order the death certificate, it will tell you if he did. If he didn’t, there’d be no point in looking up the hospital records at LMA.