For a US citizen with carry on bags only arriving at Heathrow's Terminal 1 at 11:45 how long can one expect to clear customs. We would like to make a 13:48 train from the airport to Paddington.
It's not Customs you have to be concerned about, it is Passport Control. If your flight lands more or less on time, and if the queue for the non-EU passengers for Passport Control is not too, too long, you have a good chance to make the 13:48 train. Customs is a piece of cake. Just walk through the Green "Nothing to Declare" channel, that is, if you have nothing to declare.
If passport control isn't too bad, and your plane arrives on time....you could make an earlier train.
My best time through Heathrow was 35 minutes from deplaning to getting on the tube. That was a long time ago.
Couple of points - we did this about 4 weeks ago with a flight that was to arrive at noon but we landed about 30 mins early. The deplaning and walk to immigration took between 10-15 minutes - it was a very long walk. The actual immigration and customs took about 2-3 minutes.
Why the concern about the 13:48 train? My assumption is you will probably be on a train well before 12:20 depending obviously on when your flight arrives.