The baptism register shows his date of birth as 2 February 1795, so he would have been 64 at burial in March 1859, as stated in the burial register. If the London City death is his, his age in the index (67) is three years adrift, probably an acceptable margin of error.
The burial register shows his abode as West Ham, which is also adjacent to Hackney. I can see no death registration for him in the expected quarter (or the following one) in West Ham registration district. The only other Thomas James death in a ‘London’ district in the expected quarter was in Lambeth, aged 51, which is 13 years adrift. So, again, the London City registration seems feasible.
As regards death registrations in general, whilst some are known to be missing, it is more likely that an age is wrongly reported than that a registration is missing (as suggested earlier).