A few words in defence of the Indian call centre: they have always managed to rebook me quickly when schedule changes are unfavourable to me, and been very efficient at dealing with similar basic queries. Essentially if I know what I want them to do and what I want is them to do is reasonable and within policy, they are great.
Anything off piste is a different matter. E.g. I called them earlier this week to establish the rules of adding legs to reward bookings and they got it flat wrong as my post history shows. So I do sometimes find myself begging to be put through to the UK call centre. But 75% of the time the guys in India do a great job and I certainly don't get that sinking feeling that I get with other companies when it is obvious that I'm through to the offshore call centre.
The only excellent call centres I deal with regularly are FirstDirect and Amex. Every time I call them it increases my loyalty as they are just great at what they do. My interaction with them has been consistently excellent for over a decade. I would say that BA is neutral for me: they do not excel, but they are not like the it