I've had interestingly different advice on this from the colleagues with whom I've spoken. They include, as I mentioned, a former finance secretary in the Government of India, and somebody who was also a senior official in finance.
The former finance secretary points out that banks like Lloyds and the infamous Royal Bank of Scotland do actually have very good business in India in the area of commercial services. Although the banking sector is very highly regulated in India and there are barriers to the participation of foreign banks, there are openings there. I believe that Singapore banks have also been able to enter into the areas of supplying commercial services in India, but there are a lot of detailed issues there about which I'm really not at all remotely expert.