  For two graphs $G$ and $H$, write $G \stackrel{\mathrm{rbw}}{\longrightarrow}
H$ if $G$ has the property that every {\sl proper} colouring of its edges
yields a {\sl rainbow} copy of $H$.
  We study the thresholds for such so-called {\sl anti-Ramsey} properties in
randomly perturbed dense graphs, which are unions of the form $G \cup
\mathbb{G}(n,p)$, where $G$ is an $n$-vertex graph with edge-density at least
$d$, and $d$ is a constant that does not depend on $n$.
  Our results in this paper, combined with our results in a companion paper,
determine the threshold for the property $G \cup \mathbb{G}(n,p)
\stackrel{\mathrm{rbw}}{\longrightarrow} K_s$ for every $s$. In this paper, we
show that for $s \geq 9$ the threshold is $n^{-1/m_2(K_{\left\lceil s/2
\right\rceil})}$; in fact, our $1$-statement is a supersaturation result. This
turns out to (almost) be the threshold for $s=8$ as well, but for every $4 \leq
s \leq 7$, the threshold is lower; see our companion paper for more details.
  In this paper, we also consider the property $G \cup \mathbb{G}(n,p)
\stackrel{\mathrm{rbw}}{\longrightarrow} C_{2\ell - 1}$, and show that the
threshold for this property is $n^{-2}$ for every $\ell \geq 2$; in particular,
it does not depend on the length of the cycle $C_{2\ell - 1}$. It is worth
mentioning that for even cycles, or more generally for any fixed bipartite
graph, no random edges are needed at all.
