to develop speed you need to run much shorter intervals. it isn't silly to be running intervals as short as 60 metres, quite hard, with a long slow walk back recovery.
if this sort of training is new to you, start by doing them on grass in your trainers rather than on the track, and focus on running at around your best 200m speed to begin with. as you become accustomed to them, move to the track, increase the speed gradually, and change into spikes.
after this period of acclimatisation you will benefit from varying the length of the intervals every so often. 60m for a few weeks, then 80m for a few weeks, then back down to 70m and so on.
you can run sets of these either as a stand alone session where you just concentrate on this kind of work, or you can run them before a set of longer intervals. I often run a set of 6 - 8 x 80m hard with walk back recovery, followed by 4 x 800m at 5000m pace. it largely depends on what you are training for and where in the training cycle you are.