In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $α$-Hölder continuous in time and bounded $β$-Hölder continuous in space with $α,β\in (0,1]$. The strong order of convergence of the randomised EM in $L^p$-norm is shown to be $1/2+(α\wedge (β/2))-ε$ for an arbitrary $ε\in (0,1/2)$, higher than the one of standard EM, which is $α\wedge (1/2+β/2-ε)$. The proofs highly rely on the stochastic sewing lemma, where we also provide an alternative proof when handling time irregularity for a comparison.