I do business with a LOT of indians, many of them are very educated and went to English speaking schools, listened to BBC World radio etc. They speak English with an anglicised accent but not mimicking an English person.
The women often sound particularly nice to my mind, very clean and precise English, like Edinburgh girls!
But a very few Indians do try so hard to sound like the King/Queen of England. Sometimes Indians call their fellow countrymen who try to be English 'Bounty Bars' (after the confectionery) or 'coconuts'. In other words brown outside, white inside.
The opposite of young white kids in the UK that want to sound/act like black rappers (they're known as 'whiggers', nothing to do with hair, you work it out....).
By the way, interesting fact No.1 - to make a Welsh accent, take an Indian accent and raise it an octave. Try it