The Google Books dataset suggests the crossover point was around 1905 in AmE, bu...

_delirium on Aug 3, 2014 | parent | context | favorite | on: “Theater” vs. “Theatre”: The Great New York Times ...

The Google Books dataset suggests the crossover point was around 1905 in AmE, but not until the late 1970s in BrE (modulo the usual caveats about how their data isn't necessarily a representative sample):

AmE: https://books.google.com/ngrams/graph?content=cooperation%2C...

BrE: https://books.google.com/ngrams/graph?content=cooperation%2C...