Alongside the potential new typeface, I would suggest that BA should modify its belly-coloring line, just like what KL and VN have done:
(Of course, slight changes on typefaces and color schemes were also used in the new liveries of KL and VN, but practically the old color recognition and branding were still kept)
Most importantly, this method doesn't require a significant change in the branding and the overall livery design (overall, it will not lead to a "full-scale rebranding" as concerned by the above posts), meanwhile, it is still able to introduce a refreshment to the design. Besides that, it will look sexxier on new airframes such as the 350 and 787, and they are definitely deserving better or more-suitable livery designs, don't they?
