We present the results of first experiments on the formation of collisionless shock waves (CSWs) in background plasma by injecting laser plasma bunches transverse to the magnetic field (as a piston) with a maximum energy up to per unit of solid angle and with a high enough degree of ion magnetisation. With this aim in view, on a unique KI-1 facility at the Institute of Laser Physics, Siberian Branch of the Russian Academy of Sciences (ILP), a plastic (polyethylene) target irradiated by a laser in the most energy-efficient regime (near the plasma formation threshold) and a highly ionised hydrogen plasma with a high concentration in a large volume (not less than ) have been employed. As a result of model experiments performed on the basis of a model of collisionless interaction of plasma flows, developed at the VNIIEF and being adequate to the problem under consideration, not only an intensive, background-induced, deceleration of a super-Alfven laser plasma flow, but also the formation in that flow of a strong perturbation having the properties of a subcritical CSW and propagating transverse to the magnetic field, have been first registered in the laboratory conditions.