First, tldr
In order to understand exercise and how it helps you burn calories and lose fat, you have to understand how intensity, duration and recovery work.. Once you understand these concepts, you can create you own workouts which suit you. Let's take your walk to and from work--it is about 5 km and takes you about an hour. So, in that hour, you probably burned 300 calories or so, but since you have been doing this for several months, you won't be burning many calories after you get back from work. So, you need to burn about 7700 calories to burn a kilo of fat, and if you do the math, it would take you about 26 days to burn those 7700. It isn't bad, but not what most people are looking for.
Now, you could take the long way back from work and instead of taking a half hour, you could take an hour and a half, so you would effectively be doubling your calorie burn from this activity and knocking down the time to burn a kilo of fat to 13 days. That's 2 kg per month--not bad.
Now, recovery--this is where weight training or other physical activity comes into place. When you lift weights or engage in other strenuous l activity, you literally break down your body. The body will naturally want to fix itself so it will expend energy trying to heal itself and make you stronger in the process. This is energy expenditure after your are done with the activity and this is what is going to help you the most. It doesn't have to be muscle repair which triggers this--it could be the rapid depletion of glycogen in your muscles and the body will have to replenish it (hopefully from fat in body). How does this help you without a gym? Easy, you just need to stress your body enough so it starts expending energy to you to recover. To get a good fat burning exercise, you want to look at things like
HIIT and
tabata to really get you going.
A sample HIIT ( START SLOWLY) would be to warm up for a few minutes and then find an exercise you like (jumping jacks are good here) and do them as fast as you can for 30 seconds--then walk around and catch your breath for 90 seconds, rinse, lather and repeat five times and then cool down.and you are done. You can do whatever activity you want--pushups, burpees, situps, jump rope--it doesn't matter. What you want to eventually accomplish is to reduce you rest time as much as possible so you are doing an exercise for 30 seconds and only resting for 30 seconds, or less. When you start out, take as much time as you need, but you still need to feel like you are out of breath. If you do this right, you can't do this more than twice a week, and if you go nuts, you may throw up, not a bad thing, but still sort of gross.
Other things you can to replicate this would be to find a track at a uni or where ever----walk or jog a lap to warm up and then what you will be doing is sprinting the straightaways and walking to the next straightaway and sprinting again. 4 laps and you are done. If that isn't feasible, find a somewhat isolated road on a hill--the steeper, the shorter it can be (even an underground parking entrance of building may work). Sprint up the hill and walk back down--do it as many times as you can. As you progress, you can increase the frequency and the speed you do this.
I know these are sort of nuts--what you are doing here is maximizing the effort while minimizing the time. These types of exercises stress your body and force it to expend energy long after the exercise to recover. If you are pressed for time, or can't find a gym, this is another way to go. It is much more intense, but doesn't take much time. Just start at your own pace and work your way up.
And guys regarding jump rope, it is considered a
low impact activity and puts less stress on your body and joints than activities like running. I don't know where you guys get your information because if you jump rope correctly, you are jumping just high enough for the rope to pass under your feet, which isn't much. Like any activity if done incorrectly, it can hurt you but it is something I would highly recommend (lots of videos and instructions on the youtube). The only injuries you get at beginning are from the rope hitting your legs and arms and you your pride when you can't string more than a handful of jumps in a row.