We investigate the long-run convergence of house prices across the London boroughs based on a pairwise unit root probabilistic testing procedure. In sharp contrast to the earlier literature, we employ a dataset that distinguishes between four different types of property in each borough. Using a quarterly dataset that spans from 1995 to 2014, we find evidence in favour of long-run convergence thereby suggesting that the great majority of London borough house prices are driven by a single common stochastic trend. In a further contribution, we offer new insights through analysing the determinants of long-run convergence, by considering the role of geographic proximity, type of accommodation and amenities (quality of life).