The emergence of large, fine-grained mobility datasets offers significant opportunities for the development and application of new methodologies for transportation analysis. In this paper, the link between routing behaviour and traffic patterns in urban areas is examined, introducing a method to derive estimates of traffic patterns from a large collection of fine-grained routing data. Using this dataset, the interconnectivity between road network junctions is extracted in the form of a Markov chain. This representation encodes the probability of the successive usage of adjacent road junctions, encoding routes as flows between decision points rather than flows along road segments. This network of functional interactions is then integrated within a modified Markov chain Monte Carlo (MCMC) framework, adapted for the estimation of urban traffic patterns. As part of this approach, the data-derived links between major junctions influence the movement of directed random walks executed across the network to model origin-destination journeys. The simulation process yields estimates of traffic distribution across the road network. The paper presents an implementation of the modified MCMC approach for London, United Kingdom, building an MCMC model based on a dataset of nearly 700000 minicab routes. Validation of the approach clarifies how each element of the MCMC framework contributes to junction prediction performance, and finds promising results in relation to the estimation of junction choice and minicab traffic distribution. The paper concludes by summarising the potential for the development and extension of this approach to the wider urban modelling domain.