At the time of the American War of Independence Britain was far more interested in preserving its Caribbean holdings than it was in the 'low yeild' North American regions.
And also India. If Britain had been *really* serious
about the American Revlolution, their top-flight military
talent would have been sent there, rather than second
stringers like the Howe brothers....
Another lesser know fact:
One of the unknown aspects of the Trent crisis
at the beginning of the American Civil War was that
the Union was wholly dependent on saltpeter imported
from British India. The fact that British government
halted all shipments of saltpeter to the North helped
speed the resolution of that issue.