I have recently had cause to deal with Indian call centres with three companies. (BA included).
The staff have been friendly and knowledgeable but in all three cases were unable to help me with my query and were more interested in getting me to complete a stupid survey on the quality of their service than providing a service. Total waste of time (and reflected on two of the surveys...... the third I could not be bothered to complete!).
I would rather pay to call a UK call centre than be put through to a remote centre somewhere with no true authority to help.
I hope BA make the right decision here