I am having constant pain in my left leg. The pain starts from the lower left back and left pelvic region and radiates down to the left leg. Though so?

Needs evaluation. An evaluation would need to be done. Do you know of any unusual activity or other possible cause? The muscles and nerves in the lower back/hip region are many and complicated. Misuse can be subtle - sitting oddly or too much, even stuff in back jeans pocket can press on them and cause this sort of thing. A physical therapist or massage therapist can Dx and treat. Meanwhile, try heat/rest/gentle.