Which island nation which was once a british colony and part of Malaysia is located off the tip Malay peninsula?

The island nation you are referring to is Singapore. Singapore was a former British colony and was a part of Malaysia from 1963 to 1965. It is located off the southern tip of the Malay Peninsula and is separated from Malaysia by the Johor Strait. Singapore is a sovereign city-state and has been an independent country since its separation from Malaysia in 1965.