Catalyzes the covalent attachment of ubiquitin to other proteins. Mediates the selective degradation of short-lived and abnormal proteins. Functions in the E6/E6-AP-induced ubiquitination of p53/TP53. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [E2 ubiquitin-conjugating enzyme]-L-cysteine = [E1 ubiquitin-activating enzyme]-L-cysteine + S-ubiquitinyl-[E2 ubiquitin-conjugating enzyme]-L-cysteine. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [acceptor protein]-L-lysine = [E1 ubiquitin-activating enzyme]-L-cysteine + N(6)-monoubiquitinyl-[acceptor protein]-L-lysine. Protein modification; protein ubiquitination. Interacts with SCF (SKP1-CUL1-F-box protein) E3 ubiquitin ligase complex. Belongs to the ubiquitin-conjugating enzyme family.