The so-called "British Airways Flight Operations Department Notice" is a fabrication from the mid 1970s created by a BOAC pilot, who circulated it in a slightly different format as part of an unsuccessful campaign against the merger of BOAC, BEA and several other smaller carriers into British Airways. I have all the original files from that period.
The same notice was 're-issued' by some joker in the late 1990s. At that time, the 747 Classic fleet was the only remaining* BA unit that didn't routinely fly monitored approaches. (I think they did for weather worse than Cat1 *and I don't know about CCDE.) When the Classic fleet did eventually 'catch up', someone posted the notice as a tongue-in-cheek riposte.
Having flown for different airlines and experienced both approach methods, I would agree with most of the others that the monitored approach unloads the Landing Pilot and informs him/her at an earlier stage as to the likelihood of a landing or go-around. The other crew member will be locked on to the instruments and will perform a go-around if there is no clear communication or any ambiguity at minima.
As far as reverse thrust lever handling is concerned, giving control of the TRs to the PM enables the Landing Pilot to concentrate on steering and braking. The PM will monitor the Speedbrake/Spoiler and TR deployment, N1/EPR, and give the PF the amount of reverse required. He/she will also monitor autobrake disconnection and call the speeds. That list shows that the PF is relieved of quite a few duties and can look outside all of the time. The PF can also ask for 'reverse idle' or 'forward idle' if any steering difficulties arise. The same SOP is used for an RTO.
Having said all that, my understanding is that the BA A380 fleet is about to change the SOP and have the PF operate the TRs!