BA I believe do a monitored approach on every leg. Basically the other guy will take over at minimums and land. FO or Capt. I also here that they can only disconnect the autopilot when fully configured and fully established.
"Yes" to monitored approach, but otherwise as solitaire has pointed out you've been misinformed.
In BA the pilot flying the approach is certainly allowed to hand fly if conditions permit, and the "Landing pilot" can take control anytime, regardless of configuration, as long as he/she's got the required visual references.
Regarding the use of flight directors ( sabenaboy's question) - most leave them on into LHR, a few turn them off on a good day. On "my" fleet there's plenty of opportunity for non-F/D hand flying on the Caribbean sectors.
Autolands: Now covered in the recurrent simulator details, no requirement to do any for recency on the aircraft.