No it wasn't. Lebebsraum has the relativly specific meaning of living space, for the nationals of the home country, gained by moving or killing the original population. The British Empire was used as a captive market for British industry, and to supply raw materiels and troops, not to provide living space.

Also it seemed a better idea at the time to turn it into Sir-Henry-Mackensie-istan than to let the French do something similar....

The British Empire wasn't made up of sints, but there's no need to make it out worse than it was.