I feel like I used to know this ~
Flight from US to LHR, connecting to another UK destination.
Assume immigration/customs is in London?

Immigration is definitely at Heathrow. If your luggage is checked through to your final destination, then technically customs for your checked bag is at that final destination - - though you still need to exit the customs area (with only your carry-on - - usually a stroll through the park) to get to your connecting flight.

Thank you!