There were a lot of odd Sunday only route extensions / variations (and some routes that ran Sunday only) at one time - a lot of these were tidied up in the late 70s as part of the 'Busplan' changes.
There were a variety of reasons for this - partly (as has been mentioned) to provide crew access to facilities when cafes / public toilets were closed (most meal reliefs were at home garage, although with most things LT there were exceptions), sometimes to balance the proportion of Sunday work (either OPO / crew or in general) between garages, sometimes to create routes where X number of round trips would be the right amount of time for a Sunday duty.
Some Sunday variations were actually to cater for passenger needs (at one time, a lot of routes had summer Sunday extensions in to the countryside, or to Hampton Court) or for hospital visiting, as was (indirectly) the case here.
The 126 Sunday variation was to allow the 124 to be diverted (as 124A) to Bexley Hospital on Sunday afternoons for visiting hours. As of early 1970, the Sunday 160A covered the Falconwood bit of the weekday 124 (and was extended to the old Plumstead Garage and at the other end covered the Lower Sydenham bit of the weekday 180 - this stopped when the 160 and 160A went one-man as the Lower Sydenham terminus involved a reverse, and the 160A was curtailed at Catford Garage), and the Sunday extended 126 in turn covered the Falconwood Way / Welling Way bit of the weekday 160.
There must have been a good reason (possibly to do with getting duty lengths right) for not just extending the 126 over the Welling end of the 124 route.
There's a map on the route 160A page of Ian Armstrong's London Bus Routes site
here that shows the position in 1970.