It is shown that the class of perturbations of the semigroup of shifts on L²(ℝ₊) by unitary cocycles V with the property V _t - I ∈ s₂, t ≥ 0 (where s₂ is the Hilbert-Schmidt class) contains strongly continuous semigroups of isometric operators, whose unitary parts possess spectral decompositions with the measure being singular with respect to the Lebesgue measure. Thus, we describe also the subclass of strongly continuous groups of unitary operators that are perturbations of the group of shifts on L² (ℝ) by Markovian cocycles W with the property W_t - I ∈ s₂, t ∈ ℝ.