Morden Cemetery was renamed Battersea New Cemetery (for reasons unknown, as, as you say, it isn’t in Battersea) although it was Morden when Alan Reed was buried there on 9 November 1918. The census returns suggest it was all Wandsworth at the time, but I can only guess at possible boundary changes during the last 100 years. The family had links with St Luke’s, Ramsden Road, SW12, but, presumably, there wasn’t room there ? There are 80 WW1 graves at Morden, and more than twice as many WW2 graves.
There are other discrepancies in records: the SE 5a is noted as D6032 also (presumably because it was recorded as ‘6032’, and both D6032 & E6032 were SE 5as ?); Reed’s army units are recorded as 4th Buffs (not 2/4th), 16th Londons (‘Queen’s Westminsters’ on CWGC – 16th Londons were the Queen’s Westminster Rifles) and 17th Londons (Popular & Stepney Rifles) (implying 1/17th or 2/17th – both overseas in 1917 and not 17th Training Battalion), and Reed’s record of service notes him posted to 49 Squadron at Harling Road and not 94 Squadron.