In a podcast with Joe Rogan, Jimmy Carr made the claim that:
Whaling was the biggest industry in the world in 1903.
However, some people in the comment section dispute this, claiming that Carr meant to say 1803 rather than 1903. I can't find any sources to confirm the claim, and I do find it potentially strange that whaling would continue to be so predominant even after the invention of electric light 24 years earlier in 1879.
Since Carr didn't define exactly what he means by "biggest", any relevant metric is acceptable, i.e. biggest by GDP, biggest by employment, biggest by share of global trade, etc.