We consider time discretisation of the Stokes equations on a time-dependent domain $\Omega(t)$ in an Eulerian coordinate framework. Our work can be seen as an extension of~\cite{LO}, where BDF-type time-stepping schemes were applied and analysed for a parabolic equation on time-dependent domains. For space discretisation, a geometrically unfitted finite element discretisation is applied in combination with Nitsche's method to impose boundary conditions. Physically undefined values of the velocities at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We give some insights into the stability and the a priori error analysis in space and time, which is complicated by the fact that the velocity $u(t_{n-1})$ from the previous time $t_{n-1}$ is not discrete divergence free with respect to the domain $\Omega(t_n)$ at the current time $t_n$. As a result, we obtain optimal error bounds for the velocities and a suboptimal erround bound for pressure. Finally, the theoretical results are substantiated with numerical examples in three space dimensions.