Let \(BUC(E)\) be the Banach space of all bounded real-valued, uniformly continuous functions on an infinite-dimensional separable real Banach space \(E\). Let \(P(t)\), \(t\geq 0\) be the Wiener semigroup defined on \(BUC(E)\). By a new method the authors extend the 1998 Desch-Rhandi discontinuity result given for \(P(t)\) in the Hilbert space \(E=H\). Namely, they succeed in deducing the discontinuity result: \[ \|P(t_0+ h)- P(t_0)\|_{BUC(E)}= 2,\quad\forall t_0\geq 0,\quad h>0,\quad E\text{ any Banach space}, \] from the well-known orthogonality result for the Gaussian measure \(\mu_t(\cdot)\overset{\text{def}} =\mu(\cdot/\sqrt t)\) (\(\mu\) be a centered Gaussian measure on \(E\)), namely \(\mu_t\perp \mu_s\) if \(t\neq s\). By the same new method they succeed to get an analogous discontinuity result for the more general Ornstein-Uhlenbeck semigroups (but on the Hilbert space \(E=H\)) defined with respect to some selfadjoint operator \(Q\) and some \(C_0\)-semigroup \(S(t)\). They deduce this result from the known Feldman-Hajek orthogonality criterium for general Gaussian measures on \(H\). Realizations of this result for the case of commutativity of \(Q\) and \(S(t)\) as well as for Ornstein-Uhlenbeck hyperbolic systems are given. Finally, the authors give the discontinuity result for the stopped transition semigroup associated with some Ornstein-Uhlenbeck semigroup and some stopping time random variable.