The question is wholly equivalent to "I have booked a BA flight, is it possible to change the dates". BAH come with an infinite variety of change and cancellation conditions. Some are changeable for no fee, some will have a fee which may affect the flight component, the hotel component, the car component if there is one, or any combination of the above. Some can be cancelled and some technically can't be though as the OP rightly note, so far at least (there is no guarantee that this will be the policy forever), even for a non cancellable holiday, if you don't pay the balance, BAH will simply consider that you have forfeited your deposit and won't chase you for the balance.

If the OP booked the BAH on the phone, the agent will have read the change and cancellation conditions (they are obliged to), if booking online, as with everything BA, those change and cancellation conditions are hidden in counter-intuitive places to click and hard to see.

Either way, answering yes or no or throwing in figures is going to be entirely unhelpful and inaccurate here because the only valid answer to the "is it possible and what are the conditions" is "it depends" and the only way to find out is to call BAH and ask.