cadence is how many steps per minute you make. if you have a slow cadence, then you make fewer steps, so to run at a specific pace you have to make longer strides. If the cadence was really low you would have to jump several meters in the air and crash in to the ground. With a high cadence it is like spinning your bike in a low gear, very little stress.
Awesome explanation, thanks. So basically, higher cadence will be less leg shock for me. I need to stick around 13 minute/mile, I find that gives me a gentler jog with shorter strides. I must say though it does look a bit wimpish. Longer strides looks better.

And when (or more like 'if') I'm at some point in the future able to sustain faster paces, say around 8 or 9 minute miles, my strides will be longer and I run the risk of heel strikes again, right?
I guess we have to be careful here as we're not allowed to offer medical advice, right? What I would say, I think that could be where tendons attach to the bone. Soreness will be the jarring of the muscle where it's not used to being pulled at, like shin splints.
Yes, I think that could be it, Andy. I mean, it sort of feels like the bone itself aches but I don't know if bones feel pain or just tendons and muscles. Well, after enduring the discomfort of sore quads in my first week of jogging, that has gone now. So after some rest for this latest thing, that will also hopefully disappear. Nevertheless, I better sort myself out with some better shoes, probably the same ones Ian has.