As you have an address for him in 1934, I would first check the 1939 register at FindmyPast.co.uk for him in 1939 and also for his children -- as well as Murdin try Mardin, Martin, Murden, Merton... i.e. don't assume his name is correctly recorded (or that he was using Thomas James -- try Thomas and James and all their dimunitives; and ditto his age. If you find him in 1939, you have a later date to start the search for his death... and if you don't you need to start searching in 1934.
freebmd.org.uk should be your next stop, and again you need to be creative with the search.... I can't find anything obvious but I haven't tried all the permutations and combinations. Initially I would try searching freebmd in 10 year tranches from 1934 in Deptford for the surname
m*r*n. (And then repeat for each of his children's location -- they could have passed him around).
However, I note from your other postings elsewhere that you've tried all the above (but may not have varied your search parameters); and that his status in various of his children's marriage records is ambiguous to say the least. If you didn't have the electoral roll records, I'd suggest disbelieving some or all of his children (my great-grandfather deserted his family and was recorded as dead at most of their weddings... luckily nobody cross-checked with his death sleeping in a barn a few years later).
Another place to search would be DeceasedOnline which has a wide range of burial records from local councils. A basic search is free but you have to pay to access any records.