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We investigate numerically lattice Weinberg - Salam model without fermionsfor realistic values of the fine structure constant and the Weinberg angle. Wealso analyze the data of the previous numerical investigations of latticeElectroweak theory. We have found that moving along the line of constantphysics when the lattice spacing $a$ is decreased, one should leave thephysical Higgs phase of the theory at a certain value of $a$. Our estimate ofthe minimal value of the lattice spacing is $a_c = [430\pm 40 {\rm Gev}]^{-1}$.

Upper bound on the cutoff in lattice Electroweak theory