The objective of the Enhanced Mobile Broadband use case in 5G networks is to deliver high capacity access to densely populated areas, like city centres, transportation hubs or convention centres. Millimetre-wave communications are the go-to technology to realise that objective, yet due to weak outdoor-to-indoor penetration, outdoor deployments will not suffice and dedicated indoor deployments will be necessary. In this article, we study dense deployments of millimetre-wave access points mounted on the ceiling, with directional antennas pointing downwards to illuminate selected spots on the ground. In this setup, the signal propagation is primarily limited by human body blockages. Therefore, we develop a body blockage model and derive an expression for the probability of blockage. Using the developed expressions and our simulation framework, we assess the impact of densification and body blockage on the achievable performance. We find that both coverage and area spectral efficiency curves exhibit non-trivial behaviour with respect to the access point density and that there is an optimal beamwidth-density configuration that only maximises either coverage or area spectral efficiency. Such optimal configuration changes depending on the body blockage probability, leading to a necessity for network designers to carefully consider their intended application and scenario.