From the information I gathered, the banknotes of the Straits dollar were printed by Thomas De La Rue & Company, Limited, a firm based in London. Were the banknotes of the Straits dollar printed in Britain, in India, or in the Straits Settlements?
They were printed in the UK.
The Straits Dollar was initially printed by Thomas de la Rue of London at their UK plants from 1901 until 1930:
and later, from 1931 to 1935, by Bradbury Wilkinson at their plant in New Malden in Surrey:
The Straits Dollar was replaced by the Malayan dollar in 1939, at an exchange rate of 1:1
In fact, even after independence, Singapore currency notes continued to be printed in the UK right up until 1984:
Singapore’s currency notes were initially printed in the British plants of Bradbury Wilkinson & Co Ltd and Thomas De La Rue Ltd. In 1984, Thomas De La Rue established a plant in Jurong for the printing of Singapore currency notes