Standing in a dusty street in the village of Kanadukathan in Tamil Nadu, it’s easy to imagine you’ve been transported to a film set before the action begins.

The place is deserted, but stretched out in front of the main square is a palace occupying several acres, a dazzling spectacle of whiteness with door and window details picked out in terracotta, green and yellow paint.

Balustrades on its roofline are topped with vases that could have been plucked from an Italian Renaissance place. A canopied entrance looks like Brighton Pavilion’s version of Chinese, and windows on the first floor have pointed Gothic arches and stained glass.

This grand building, the Chettinad Palace, is one of the most...