The British Academy does not have an OA policy, and grants cannot be used to pay publication charges.
The British Academy position is covered in the FAQ of individual funding schemes:
‘When I apply for funding through any of the awards offered by the British Academy, can I include in the application the cost of APCs (Article Processing Charges) to enable any articles that may arise from the research to be published in learned journals that offer a ‘Gold’ open access option?
No. Currently the Academy’s position is that costs of publication are not eligible costs.
Does the Academy require the outputs of the research it funds to be made available in any open access format?
No, this is not currently a stipulation of any Academy award.’