We describe a hybrid statistical mechanical and dynamical approach for modelling the formation of closed, open and elongating complexes of RNA polymerase, the interactions of these polymerases to produce transcriptional interference, and the regulation of these processes by a DNA-binding and DNA-looping regulatory protein. As a model system, we have used bacteriophage 186, for which genetic, biochemical and structural studies have suggested that the CI repressor binds as a 14-mer to form alternative DNA-looped complexes, and activates lysogenic transcription indirectly by relieving transcriptional interference caused by the convergent lytic promoter. The modelling showed that the original mechanisms proposed to explain this relief of transcriptional interference are not consistent with the available in vivo reporter data. However, a good fit to the reporter data was given by a revised model that incorporates a novel predicted regulatory mechanism: that RNA polymerase bound at the lysogenic promoter protects itself from transcriptional interference by recruiting CI to the lytic promoter. This mechanism and various estimates of in vivo biochemical parameters for the 186 CI system should be testable. Our results demonstrate the power of mathematical modelling for the extraction of detailed biochemical information from in vivo data.