On the continuous cohomology of diffeomorphism groups

Suppose that $M$ is a connected orientable $n$-dimensional manifold and $m>2n$. If $H^i(M,\mathbb R)=0$ for $i>0$, it is proved that for each $m$ there is a monomorphism $H^m(W_n,O(n))\to H^m_\mathrm{cont}(\operatorname{Diff}M,\mathbb R)$. If $M$ is closed and oriented, it is proved that for each $m$ there is a monomorphism $H^m(W_n,O(n))\to H^{m-n}_\mathrm{cont}(\operatorname{Diff}_+M,\mathbb R)$, where $\operatorname{Diff}_+M$ is the group of orientation preserving diffeomorphisms of $M$.