Hello.
Comment from Australia here. Know nothing about the specifics of your operation although I know enough about the battle of full service carriers vs. LCC airlines. BA is securing YOUR future by rotating aircraft back to base each day. Doing away away with overnights reduces costs astronomically and creates a more level playing field (comparing apples with applies) with HUGELY SUCCESSFUL LCCs. I couldn't agree with sammyhostie more.
I absolutely agree that doing away for with overnights decreases crew morale and more importantly allowances (!!!). Though in doing this your employer is securing it's own future and hence yours. I have recently been subject to a 15-20% drop in annual income from lowering average nights away from 9 to 11 per month to an average of 0 to 1. (Thanks Jetstar

) And we are working an average of an EXTRA sector per day for LESS money. But at the same time it is a absolute neccessity in order to compete and maintain profit.
I have no doubt that your company's thoughts are primarily of it's own future. But it does in turn secure your own.
Can assure you that NO airline will increase nightstops to make crew happy. Not nowadays unfortunately. Sad but true I am afraid.
It's not my intention to cheapen your totally justifiable concerns. It's just no airline anywhere in the world can afford to do anything but cut unnecessary costs - particularily full service carriers. Of which BA is one of (if not) the finest!