This paper investigates the long-run convergence of regional house prices in the UK. Using a variety of econometric methods, existing studies have failed to reach a consensus on whether or not regional house prices are cointegrated and exhibit long-run constancy relative to each other. We propose the application of a new test that combines principal components analysis with unit root testing to throw new light on the regional convergence debate. Using mixadjusted quarterly house price data for 1973-2005, we find that existing unit root and cointegration methodologies indicate the presence of multiple stochastic trends with, at best, very weak evidence of long-run convergence. However, testing for the stationarity of the largest principal component based on regional house price differentials suggests that all UK regional house prices are driven by a single common stochastic trend and can be regarded as exhibiting strong convergence in the long-run. Further analysis suggests there is a high degree of persistence in regional house price differentials.