Single-walled carbon nanotubes provide an ideal system for studying the properties of one-dimensional (1D) materials, where strong electron-electron interactions are expected(1). Optical measurements have recently reported the existence of excitons in semiconducting nanotubes, revealing the importance of many-body effects(2-4). Surprisingly, pioneering electronic structure calculations(5-7) and scanning tunnelling spectroscopy (STS) experiments(8-10) report the same gap values as optical experiments. Here, an experimental STS study of the bandgap of single-walled semiconducting nanotubes, demonstrates a continuous transition from the gap reduced by the screening resulting from the metal substrate to the intrinsic gap dominated by many-body interactions. These results provide a deeper knowledge of many-body interactions in these 1D systems and a better understanding of their electronic properties, which is a prerequisite for any application of nanotubes in the ultimate device miniaturization for molecular electronics(11,12), or spintronics(13).