The ignition conditions of cylindrical ICF targets, magnetically insulated and inertially confined by a tamper, are investigated by means of one dimensional hydrodynamic simulations. The central point of interest is the effect of the tamper on the minimum fuel ρR value required for igniting pre-assembled fuel configurations. These configurations are studied for complete suppression of heat conduction losses and full re-deposition of alpha particles in the fuel due to the magnetic field. It is found that the value of ρR required for ignition depends significantly on the tamper volume and the tamper entropy at stagnation, and that it scales with the fuel mass m per unit length as (ρR)ign ∝ m-κ, where 0.65 ⩽ κ ⩽ 1.0.