Originally Posted by
BAAZ
NB the OP's question was slightly different: he wants to fly from the UK to country X, leaving the UK on passport A and arriving in country X at the end of the same flight using passport B. You can't replace passport details *during* a flight AFAIK (even if you have on-board wifi).
Sorry, I misread the OP's question too.
I've always taken the view that it's the passport to be used at destination that's needed, and that's been my practical experience too. After all, API is sent to the destination country to alert that country to the identity of the aircraft-load of undesirables that the airline's about to transport there. And the airline will want to check that passport for entry eligibility as well.