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