First - you are only training your upper aerobic and/or anaerobic system by trying to go out as fast as you can for as hard as you can. What the pace is doesn't matter - how hard the effort is for you is what matters.
That upper range isn't about endurance until way way way down the road, you have no aerobic base to even be concerned with that side of the range yet.
Second - what cramps up exactly - legs is pretty big body part, which part of the legs?
If your stride is like the running attempt with long reach but not stepping often (turn-over), then you are just pounding yourself in to the ground, and sure cramps should be expected.
Third - get enough sodium, potassium, magnesium in your diet, drink enough water?
You could be barely on the verge of decent into terrible range, and the running just pushes your legs over the line that was pretty close already.
Slowing down takes care of much of this, as mentioned, but try to get your foot strikes to 80-90 per min if they are not.
And interval jogging / walking is great training idea - but you don't do the jog part at such a speed as you can't make it anymore. As you have proven, it doesn't actually make for good recovery.
Do about 1 min jog to 1 min walk, that's 50%. And jog, not run as in all out, jog slow holding yourself back.