This paper is focused on statistical modelling, prediction and adaptive adjustment of patient recruitment in multicentre clinical trials. We consider a recruitment model, where patients arrive at different centres according to Poisson processes, with recruitment rates viewed as a sample from a gamma distribution. A statistical analysis of completed studies is provided and properties of a few types of parameter estimators are investigated analytically and using simulation. The model has been validated using many real completed trials. A statistical technique for predictive recruitment modelling for ongoing trials is developed. It allows the prediction of the remaining recruitment time together with confidence intervals using current enrolment information, and also provision of an adaptive adjustment of recruitment by calculating the number of additional centres required to accomplish a study up to a certain deadline with a pre-specified probability. Results are illustrated for different recruitment scenarios.