I seem to remember that there are 2 reasons why BA adopt these SOP's.The main one being to standardise across all fleets and the second is because of the 10 years plus one needs to remain in the R/H seat,therefore not wanting to be seen as a lowly co pilot and a radio operator on non handling sectors.
I always found it amusing when no flight level checks were made above FL200 and this was becuase the DC3 didnt fly this high so was omitted to keep all calls standard across the board.
The non handling pilot briefs the non flying pilot on how he/she would like the approach flown.The non flying pilot then flies the approach as briefed and will remain at the controls until DH visual when the controls are handed back to the non handling pilot who the makes the landing, who by now I presume becomes the non flying pilot, BUT WHOSE HANDLING IT? Anyway the flying pilot now asks the non handling pilot for full reverse but only if thats what he briefed for at TOD,otherwise he will have to ask for idle reverse which he will brief for on the rollout I presume.I think the purser taxis the A/C onto stand and the passenger in 3A does the after landing checklist.