Since the start of the century, particularly in urban centres, housing markets worldwide have experienced stark price and rent increases. As a consequence urban agglomerations have experienced strong changes in their neighbourhood composition with originally poorer, central areas gentrifying quickly. Governments have reacted by raising the topic of affordable housing on the political agenda, and increasingly use instruments such as rent control measures. This paper directly links affordable housing policies and gentrification processes in a quantitative spatial model. The model captures the key patterns of endogenous gentrification processes and provides novel, counterfactual evidence of the impact of a large scale housing market intervention implemented in Berlin to address the consequences of rising housing prices. Further, through counterfactual analysis the paper compares alternative housing policies and their respective welfare implications.