More 'Bombayites' say 'Bombay' than do 'Britishers' these days, sort of politically incorrect here. From what I understood I thought it was variously Bombay/Mumbai locally according to political party lines.

Never heard Madras used for the location itself in my lifetime, couldn't have told you it was Chennai. It is used in describing British Indian crappy takeaway/supermarket food though (I don't mean that as a slight on the actual food of Chennai, just some of the stuff we have/invent here in the UK and give random names).