Words in the News: Bombay or Mumbai

While most of the media now refer to India's financial capital as Mumbai, you can still find references to Bombay:  

  

So, which is the correct version of the name? According to Wikipedia, the city was renamed Mumbai in 1996 by the Shiv Sena government of Maharashtra, in keeping with their policy of renaming colonial institutions after historic local names. 

Wikipedia also has a detailed explanation of the etymology of both names. Contrary to what you might think, it seems that the English name Bombay was not derived from the local name Mumbai, but from Portuguese. Any similarity would appear to be a coincidence. But that still doesn't answer the question: Why does The Times use Bombay in preference to Mumbai? Any ideas?

Update: guardian.co.uk's Organ Grinder blog has an article discussing this very question - it's more complicated than you would think! Thanks to Tim Roll-Pickering for that.