Litebulbs,
you are not quite right in the statement that
It doesn't matter what agreement BA have
as the BA scheme is approved by the regulating authority - the CAA. There are differences between CAP 371 and the BA scheme, generally they are subtle and not major, but that does not mean that CAP371 applies to BA crew.
The day off definition is fair enough, but it does not mean that it is applicable in the situation that you are suggesting it should be used. The BA definition of a day off is as follows:
DAYS OFF'
Periods available for leisure and relaxation free of all duties. A single
day off shall include two local nights. Consecutive days off shall include
a further local night for each additional consecutive day off. A rest
period may be included as part of a day off.
Note it also talks about a rest period in there, which is defined as:
'REST PERIOD'
A period of time before starting a flying duty period which is designed
to give crew members adequate opportunity to rest before a flight.
They are different things and a day off is not legally required after a long haul duty. CAP371 does not require a day off after a long haul duty either.