  We list all potential candidates for U(1) anomalous non-local 1-loop 4-point
amplitudes and higher loop UV divergences in $\mathcal{N}\geq 5$
supergravities. The relevant chiral superinvariants are constructed from
linearized chiral superfields and define the corresponding superamplitudes. The
anomalous amplitudes, of the kind present in $\mathcal{N}=4$, are shown to be
absent in $\mathcal{N} \geq 5$. In $\mathcal{N}=6$ supergravity the result is
deduced from the double-copy $\mathcal{N}=4_{YM} \times (\mathcal{N}=2)_{YM}$
model, whereas in $\mathcal{N}=5,8$ the result on absence of anomalous
amplitudes is derived in supergravities as well as in the $(\mathcal{N}=4)_{YM}
\times (\mathcal{N}-4)_{YM}$ double-copy models.
