We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied through a bootstrap of regularity to show that solutions of 2D and 3D stochastic Navier–Stokes equations retain the higher order regularity of the initial condition on their time of existence.