People in the USA and Canada have downloaded the update. Nothing for the UK yet.
Don't be confused by the Android Galaxy Wear app/ plug in which is also being released. I got it a few days ago. It's no great shakes - couple of extra settings you can set by phone and a preview watch face feature, also on the phone.
I had exactly the same problem, it didn't display heart rate while pretty much doing anything but sitting. After the update I got today, it is fixed, heart rate was working during my run without problems.