ZURICH—Last year, film producer Aashish Singh was planning overseas shooting for his Mumbai studio's latest epic, the tale of an amnesiac bomb disposal expert and the sweetheart he can't quite remember.

In one scene, the lovers soar into the clouds and croon in each other's arms, a Bollywood motif commonly dubbed the "Cut to Switzerland" because so many montages have been staged in the country's picturesque mountains. Mr. Singh's crew, however, opted for London rooftops rather than Alpine glaciers.

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