Do some HIIT style running training. And don’t diss the squats! They make your legs like steel and your gluten like iron and this will help with speed too.
Try jumping squats - a full squat into a jump.
For HIIT training I do stuff on the treadmill - working on either increasing speed or increasing incline.
For example: start at 8kph & an incline of 2. Warm up at that for a couple of minutes.
Then do a pyramid going up either speed or incline over the next few minutes.
Run for say, 45secs at 9kph then jump off for 15 secs and put the speed up to 10kph. Do 45 secs then jump off for 15. Put the speed up to 11kph. At that speed I would run for 40 secs on,20 secs off.
At maybe 13 kph I’d run for 30 secs on 30secs off.
I’ve done this up to 16kph where I could only manage 20secs - I freaked myself out about the speed so I keep going back to that to get more used to it.
When you get to the fastest speech Ed you can bear, that’s the top of your pyramid and then you work your way down.
The one tricky thing you have to learn is how to jump off the treadmill and get back on. Basically, grab the sides with your hands and then jump your feet off the band onto the sides of the machine. To get back on the moving treadmill, support yourself with your hands and start running until you’re up to speed then let go of the sides. It’s a bit like the cartoon running in the air!
You can do the same exercise with the incline. Start running at day 8kph and then do the same 40secs on, 20secs off and increasing the incline each time while keeping speed the same.
You only need to do 10 minutes of this regularly -maybe once a week or once a fortnight? - and you WILL get faster.
My treadmill jogging rate doing C25K used to be 5kph warm up then about 8kph jogging. I now can run (on the treadmill) at 10kph quite comfortably.
Well - “comfort” is a relative term .... 