I had exactly the same issue, my heart rate would go 150-160BPM the moment I switch from fast walking to slowest possible jogging.
I was doing some running between mountain trips and just gave up running on low pulse. It seemed that there is nothing possible to fix it, and doctors ensured that I have no heart deficiency of any kind. I never met anyone who had a similar problem, it seemed to be “abnormal” just for me, my pulse was higher than even amateurs to running.
However, I am following the Training plan set up by John, after 3 months I am now able to jog with 120-125 pulse. In the beginning, this probably seemed very funny – me trying to simulate running at lowest pace, like a slow-motion movie.
I need to admit, I was not doing very long aerobic training under the current program, and dont know how big was the impact of other exercises ( intervals, core & max strength) on my current performance.