Upvote:1
Your BRP is evidence of your immigration status in the UK https://www.gov.uk/biometric-residence-permits You will have to show it along with your valid national passport before you begin your return journey, and again when you re-enter the United Kingdom. The permit proves that you are allowed to return to the United Kingdom, but it cannot be used instead of a passport.
Since your US passport is valid, it is sufficient alongside your BRP.