The cells in our tissues go through many divisions during our lifetime. Every time a cell divides, there is a possibility that it collects a mutation. If these mutations accumulate they can cause cancer. How can multicellular organisms maintain their tissues' homeostatic function and keep the risk of cancer sufficiently low? According to our former results in hierarchically organised tissues divisional load (the number of divisions along cell lineages) can be greatly minimised in order to avoid the accumulation of somatic mutations. Here we extend our model to take into consideration the fact that the cells interact with each other. In this model the rate of the different types of divisions depends on the number of the cells on the hierarchical levels. Normally, this regulation prevents the tissue from growing bigger than its homeostatic size. Using simulations we examine the conditions necessary for the emergence of cancer by introducing mutations that increase the rate of different types of cell division events. When cells only undergo symmetric differentiation and symmetric division, and are not able to differentiate asymmetrically, it is harder for mutations to be fixed in the cell population. The reason behind this is that the critical number of mutations for the fixation is higher. Our results indicate that tissue size regulation considerably amplifies this effect and results in a surprisingly large reduction in the occurrence of cancer if the cells in the tissue do not undergo asymmetrical divisions.