The roots of this conflict go back far further than the British Empire. The region was Hindu, then Buddhist, then conquered by the Muslims, then became part of a Sikh empire , then under Sikh/British control......
The Maharaja of the area (a Sikh aligned to the British) was the one who refused to cede to Pakistani control (during separation), and asked for help from the British and Hindus.
It is an issue that is far more complex than British colonialism!