The British had nothing to do with the partition. Once they started to withdrawal, the Muslims and Hindus started attacking each other. Muslims did not trust the Congress Party, which had a lock on the post independence government. Over 2,000,000 people died before the British negotiated a partition agreement to slow the killing.
They have since fought several wars. The most recent was the Kargill War in 1999.
But:
"The British had nothing to do with the partition.....Over 2,000,000 people died before the British negotiated a partition agreement"
So they kind of, sort of did have some hand in the partition, although it's true they didn't mandate it.