A heat transfer model based on the well-known Henderson's equation has been enhanced to allow ignition and combustion phenomena of fibre-reinforced structural composite materials to be predicted from first principles using known physical and thermodynamic data for their constituents. This enhancement has consisted of two principal components; 1) a mathematical mechanism for recognition of the accurate time to and temperature of ignition, and 2) an incorporation of the heat of combustion generated during the exposure time of interest. This has allowed a model of good qualitative character to be achieved, which generally replicates mass and temperature data obtained by cone calorimetric experiments for two types of composite laminates, a control E-glass / epoxy composite and a fire retarded laminate, where the resin contains fire retardant chemicals as additives. There however remains the challenge of improving the quantitative fit of the model by obtaining more accurate volatiles diffusivity / permeability parameters, as well as a fully representative quantitative understanding of the volatiles released during decomposition of the two different composite materials. It is anticipated that both these measures will result in a model of more accurate quantitative fidelity to cone calorimetry data, which may ultimately be used as a partial substitute for experiment in the early stages of composite formulation and fire testing.