The premise contains a historical error: the British Empire did not control "Pakistan" because Pakistan did not exist until 1947. The British Raj governed the entire Indian subcontinent—including the regions that became Pakistan (West and East Pakistan, now Bangladesh). Upon independence in 1947, British India was partitioned into the dominions of India and Pakistan. So the British extracted resources, labor, and strategic value from the Indian subcontinent, not from a country called Pakistan.