I feel sorry for the people in those call centres. They're simply doing the job they've been given. In my opinion, the blame lies with companies who want to export their call centres to countries where they can pay a paltry amount in wages and who give the call centre staff rigid, useless scripts from which they are not allowed to deviate.
I have been driven to distraction during calls to such call centres but I really try not to take it out on the person on the other end of the phone because I'm aware that there is nothing they can really do - if they deviate from the script, they could lose pay or even lose their job. However, I can assure you that there is little more frustrating than someone repeatedly saying "I am very sorry that you are having problems with your computer/washing machine/mobile phone, Miss [surname], in response to everything I say. They appear to be ordered to keep talking, no matter what. I'd rather have 30 seconds of silence if I thought the person was genuinely working to try to fix my problem.
I have heard of train companies in the UK moving their call centres to other countries with somewhat disastrous results. There are stories of people telephoning to ask for times and fares for a relatively simple journey between two stations that are perhaps 20 miles apart, and being give a route that takes them over 200 miles out of their way and costs 5 times as much as the actual fare. The problem seems to be that the person in the call centre has absolutely no idea of the geography of the UK so it's easy for them to not realise that the route and cost involved couldn't possibly relate to the two stations in question (and of course they can mishear or misspell stations they've never heard of), resulting in totally inaccurate results.
As the others have said, the people in Indian call centres don't "impersonate" people from the UK, America etc. Their accents and sometimes even the noises in the background of a call give them away immediately. However, they certainly are told to use (or are given) very English-sounding names to use. We are not fooled.