The emission inventory for London indicates that nearly 80% of the particulate emissions derive from vehicular sources. Most of this mass is in the form of ultrafine submicrometer particles which are of concern because of their influence on lung function. The prediction of their dispersion in the atmosphere coupled to the physical and chemical transformations which affect their size distribution and concentration are of great importance. This paper reports the first results from a new meso-scale Lagrangian model which follows the particulate emissions and the evolution of their size distribution across the city. The vehicular emissions are based on the published inventory, corrected to time of day, while other emissions are assumed steady. The initial size distributions of background and emitted particles are represented by the sum of three lognormal distributions. Meteorological data are derived from Meteorological Office reports and are preprocessed to obtain the hourly values of boundary layer depth, Monin-Obukov (MO) length, friction velocity, etc., needed for the computation of the vertical dispersion process via eddy diffusivities and the aerodynamic component of the dry deposition process. In the vertical direction, three layers are assumed-surface layer (typically 50 m), canopy layer and one further layer up to the prevailing boundary layer depth. Currently, the model includes wet and dry deposition and coagulation but not chemical reaction, nucleation or deliquescence. Trajectories are evolved for several hours across the city and the number size distributions and mass concentrations (PM10, PM2.5, PM1 and PM0.1) output at each step. This enables the vehicular contributions over and above the background concentration in each size range to be studied in detail. Data from the model have been compared with experimental data for one of the London background sites where particle number size distribution up to 450 nm (SMPS), plus PM10 and PM2.5 (TEOM) data are available.