Optimising spacecraft reorientation manoeuvres with respect to time, energy and propellant is essential for achieving a high mission performance. Solving this reorientation problem in real time and onboard is considered to be a promising opportunity to achieve further efficiency improvements in space missions. However, the nonlinear programming (NLP) methods that are currently used are too slow for onboard implementation. Therefore, in this study, a sequential convex programming (SCP)-based optimisation algorithm was developed to solve the spacecraft reorientation problem in real time. Several features are implemented and proposed to improve the algorithm performance compared to existing studies, amongst others: an alternative transcription technique, a method to reduce inter-nodal constraint violations and an improved initialisation strategy. Furthermore, an extensive Monte Carlo campaign was conducted to thoroughly assess the performance of the SCP algorithm. While showing similar performance in terms of robustness and optimality, the median computational efficiency of the SCP algorithm was found to be up to a factor 6.1 higher than a state-of-the-art NLP benchmark algorithm. All results considered, it can be concluded that SCP-based optimisation algorithms are a promising candidate for solving the spacecraft reorientation problem onboard.