Precise pressure experiments in supercooled bcc 4He are carried out under cooling along an isochore near an equilibrium line of the bcc-hcp structural phase transition. It is established that the transition from bcc to hcp occurs after significant delay which can be of a few seconds to a few hours depending on the extent of supercooling. The data obtained allow to establish of a line of maximum supercooling in the P-T phase diagram and to describe it within the framework of homogeneous nucleation theory. It is shown that the reverse hcp-bcc transition occurs without any delay, i.e., this structural phase transition is strongly asymmetric. The additional peculiarities are observed in the pressure and temperature time dependences. The possible reasons appearing of them are discussed