A new and flexible velocity-map ion imaging apparatus, designed for the study of photodissociation processes and photon-initiated bimolecular reactions in a single molecular beam, has been constructed, developed and characterised. An image Legendre moment fitting analysis was developed to allow recovery of centre-of-mass (CM) angular scattering and kinetic energy release distributions from velocity-map ion images of the products of photon-initiated bimolecular reactions. The Legendre moment analysis methodology has been applied to images of the HCl(v' = 0,j' = 0-6) products of the reactions of Cl(²P_3/2) atoms with ethane and n-butane at collision energies of 0.24 eV and 0.32 eV respectively. The Cl(²P_3/2) reactants were generated by polarised laser photodissociation of Cl₂ at 355 nm. For reaction with ethane, the CM angular scattering distributions show a steady trend from forward scattering at low j' to more isotropic, but backward peaking, scattering at high j'. An impact parameter-based mechanism is proposed to account for the observed dynamics. Abstraction of a hydrogen atom from a primary carbon site in n-butane is seen to produce rotationally very cold HCl products that are forward scattered, whereas H atom abstraction from a secondary carbon site in n-butane yields more isotropically scattered HCl products formed with higher rotational excitation. A peripheral mechanism is proposed to operate for the primary abstraction channel, whilst a more rebound type mechanism is seen to account for the dynamics of the secondary abstraction channel. Around 22% and 30% of the available energy is found in internal modes of the alkyl radical co-products of the Cl + C₂H₆ and Cl + n-C₄H₁₀ reactions respectively. Possible sources of alkyl co-product excitation are discussed in each case. The hydrogen or deuterium atom abstraction reactions of Cl(²P_3/2) with CH₄, CD₄ and CH₃D, have been studied at mean collision energies around 0.3 eV. Chlorine atom reactants were generated by polarised laser photodissociation of Cl₂ at 308 nm. The methyl radical products were detected using (2+1) resonance-enhanced multi-photon ionisation, coupled with velocity-map ion imaging. The laboratory frame speed distributions obtained from the images are in excellent agreement with previous work. The interpretation of the experiments is shown to be very sensitive to assumptions made about the reactant velocity distributions. If these are assumed to be narrow, the data are seen to suggest that a significant fraction of the product signal must arise from the reaction of Cl with vibrationally excited methane reactants. This conclusion is in agreement with previous photon-initiated reaction studies. However, by allowing for the spread in collision energies in the molecular beam, it is shown that it is possible to fit the data sensibly assuming reaction with vibrational ground state methane alone. CM angular scattering distributions thereby derived are presented for all three reactions.