Can you lose fat on exercise alone?
Losing weight is almost totally driven by food choices (what and how much). Exercise (such as walking, running, and workouts) is needed for stamina and strength and for making sure that the weight you lose is fat and not muscle, but purely in terms of weight loss, exercise is neither necessary nor sufficient. It's not necessary, because even if you don't exercise, you can lose weight; and it's not sufficient because, even if you do exercise, you cannot eat anything you want and still lose weight.
In contrast, good food choices are both necessary and sufficient for weight loss, so I see food choice as the main driver of weight loss.
My current diet advice describes in some detail an approach that is simple, easy, effective, satisfying (you won't feel hungry), involves no calorie counting, and offers an easy transition from weight loss to weight maintenance, always tricky. I lost quite a bit of weight following that method, and I was quite sedentary at the time. (Since then I have taken up Nordic walking and because it's so enjoyable I now walk a little over an hour a day, six days a week. But weight loss still depends on food choices. Walking is for fitness, not weight loss.)
It will probably take a couple of weeks to get the hang of it, but stick with it for two months and see then what you think.