I do intervals of 2 minutes of jump rope with a 1 minute break in between each interval, during which I walk around briskly. Will this improve my long distance running time?
It's possible that it will improve your time, but not because you are getting in better running shape. Rather, you are working on your calf strength and rebound ability. This in turn should result in a slightly more efficient running stride.
However, as brent points out, it's not a substitute for running, and any gains that you might make are at best going to be 1-2 seconds off of your current pace. The best advice I've ever seen for endurance running is "Run. Run lots. Mostly slow, sometimes fast".
The biggest mistake that amateur runners make is their easy runs are often at too hard a pace, and their hard runs are not hard enough. I would recommend using the Macmillan running calculator or similar, and figuring out what your goal paces and distances should be, based off of any events that you might be training for.
As a cross training activity jumping rope is a fantastic activity. It will give you some cardio benefit as well as calf and leg strengthening. However this alone will not get you to the end of a long run.
The best way to train for a long run is to run. You should schedule one long run each week at 60-90 slower than you anticipated race pace. The idea behind this is to build you aerobic stamina while also getting your legs used to the time and distance you will be running.
I'm not a trained professional who can back that up with proper biomechanics, but I run 10 km/week and currently jump rope daily, and I strongly believe that the answer is unequivocally yes:
Jumping rope will force you to work on posture (form) and coordination. The additional strength in your core will help with keeping good form while running.
Jumping rope boosts your cardio, and can be done in a way to boost it a lot (see boxing). However, I'm not advanced enough to say that it's the best way to do so, or to give you measured improvements.
Despite being a low-impact sport, jumping rope strengthens your lower/leg muscles, a lot. If you dose your cross-training properly, that must certainly help preventing a bunch of running-related injuries.
Jumping rope is a complete form of physical activity. I'm positive that it's helping a lot with my own running.