Joint European Torus (JET) plasma initiations that form a significant quantity of runaway electrons have been studied. It is shown that there is no direct relationship between the prefill pressure and breakdown electric field and signs of runaway electrons during the plasma initiation. Runaway electron generation is determined by the electric field and density development at and after burn-through. A clear criterion of density and electric field at one given point in time, which would ensure the avoidance of runaway electron generation, cannot be determined, because the timescales for the formation of runaway electrons and for the dynamics of the density differ significantly. Moreover, the formation process can be reversed, reducing the influence of runaway electrons on the discharge. Ensuring a high enough density will reduce the likelihood that runaway electron discharges are formed. It is also found that at JET the electric field often exceeds the critical electric field during the early stages of the current ramp-up phase, even when no signs of runaway electrons are present. Expected runaway current dynamics have been analysed using the discharge circuit equation. The comparison of the expected runaway electron current dynamics shows it to be significantly slower compared to theoretical expectations in the presence of a hot and dense thermal background plasma. This could be explained by an enhanced critical electric field and/or a reduced confinement of runaway electrons. The latter is shown to be affected by bursts of magnetohydrodynamic activity that are characteristic during the current ramp-up. The development of discharges in which the current is fully carried by runaway electrons happens on a slow timescale of several seconds, limited by the available flux. Such timescales are sufficient for improved active control of these events, avoiding runaway currents at plasma initiation exceeding values at which they could damage in-vessel components. The results provide insight into the improvement and interpretation of self-consistent modelling of runaway electron generation during the start-up of International Thermonuclear Experimental Reactor discharges.