does anyone feel slightly uncomfortable about this... 

I'd say more than 'slightly'. I know it has been going on for a while already with other call centres for British firms. Getting away from the costs thing there has already been problems link - Indian call centre staff 'selling bank details' and of course 'data negligence' as well.

I also wonder if those who are 'all for it' would be so enthusiastic about it if it was their job on the line.

I agree with Boudi about the reinvesting the money in their own region.

As costs are an issue though, perhaps this might be a better option? link - Prisoners in English jails are working for a range of public services