To be fair, BA are an airline, a PLC, operating in a competitive environment and answerable to their shareholders. There is no obligation on them to contribute company resources to the preservation of ex-fleet aeroplanes and the shareholders might legitimatly object if the airline did that.
A parallell can be seen in railway preservation. The most the preservationists can hope for is that the railway companies might donate time-expired locomotives and stock to them, but often this doesn't happen, and the preservationists have to outbid the scrap man for these. There is certainly no financial support for railway preservation from rail companies - the most they'll do is occasionally paint a locomtive in 'heritage' livery.
The railway preservation movement is self-supporting, with many voluteers and preserved railways run as businesses to remain viable. Though we, as aircraft enthusiats, may wish it were otherwise, why shouldn't the same apply to aircraft preservation?