The strong variability of magnetic central engines of active galactic nuclei (AGNs) and gamma-ray bursts (GRBs) may result in highly intermittent strongly magnetized relativistic outflows. We find a new magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state flows. This impulsive acceleration results in kinetic-energy-dominated flows that are conducive to efficient dissipation at internal magnetohydrodynamic shocks on astrophysically relevant distances from the central source. For a spherical flow, a discrete shell ejected from the source over a time t0 with Lorentz factor Γ∼ 1 and initial magnetization σ0=B20/4πρ0c2≫ 1 quickly reaches a typical Lorentz factor Γ∼σ1/30 and magnetization σ∼σ2/30 at the distance R0≈ct0. At this point, the magnetized shell of width Δ∼R0 in the laboratory frame loses causal contact with the source and continues to accelerate by spreading significantly in its own rest frame. The expansion is driven by the magnetic pressure gradient and leads to relativistic relative velocities between the front and back of the shell. While the expansion is roughly symmetric in the centre of the momentum frame, in the laboratory frame, most of the energy and momentum remains in a region (or shell) of width Δ∼R0 at the head of the flow. This acceleration proceeds as Γ∼ (σ0R/R0)1/3 and σ∼σ2/30 (R/R0)-1/3 until reaching a coasting radius Rc∼R0σ20, where the kinetic energy becomes dominant: Γ∼σ0 and σ∼ 1 at Rc. The shell then starts coasting and spreading (radially), its width growing as Δ∼R0(R/Rc), causing its magnetization to drop as σ∼Rc/R at R > Rc. Given the typical variability time-scales of AGNs and GRBs, the magnetic acceleration in these sources is a combination of the quasi-steady-state collimation acceleration close to the source and the impulsive (conical or locally quasi-spherical) acceleration farther out. The interaction with the external medium, which can significantly affect the dynamics, is briefly addressed in the discussion.