Many if not most tissues need a controlled number of stem cells to maintain normal function. Cancer can be seen as a process of disturbed tissue homeostasis, in which too many cells have or acquire too primitive identity. Here we measured how oncogenes and tumour suppressors affect the differentiation capacity, proportion and characteristics of progenitor cells in a model tissue. Neural progenitor cells (NPCs) were exposed to human papilloma virus E6, E7 or E6/E7 oncogenes, which degrade tumour suppressors p53 and pRb family members, respectively. E6/E7-expressing or p53−/− NPCs were able to differentiate, but simultaneously retained high capacity for self-renewal, proliferation, ability to remain multipotent in conditions promoting differentiation and showed delayed cell cycle exit. These functions were mediated through p53 and pRb family, and involved MEK-ERK signalling. Decreased amount of p53 increased self-renewal and proliferation, whereas pRb affected only proliferation. Our results suggest that the oncogenes increase whereas p53 and pRb family tumour suppressors decrease the number and proportion of progenitor cells. These findings provide one explanation how oncogenes and tumour suppressors control tissue homeostasis and highlight their importance in stem cell self-renewal, linked both to cancer and life-long tissue turnover.