Recently I arrived from the US into Heathrow, perhaps terminal 4 but I
don't recall for sure. I was confused by the signs and I am wondering
what I should have done.

I hold a UK passport and my itinerary had a connecting flight. However,
I wasn't yet checked in for the connection, nor was my baggage checked
through beyond LHR.

So, just before passport control, there was a sign pointing left for UK
passports and right for flight connections. Which way should I have
gone, and why? I was confused because both directions seemed to apply!
But then I worried that if I followed flight connections, I didn't know
I would get to pick up my bag to get it onto the connecting flight, so I
followed the UK passports sign and ended up picking up my bag and going
landside and then I went and found check-in for my next flight, I just
didn't know if I'd needlessly gone the long way around.

-- Mark