 Nonaffine special fibre obtained by blowing up

Blow up $(0,1,0)$ in ${\mathbb{A}}_{x,y,z}^3$ and compose with $xy:{\mathbb{A}}^3\to {\mathbb{A}}^1$. Nonzero fibres are ${\mathbb{G}}_m\times {\mathbb{A}}^1$. The zero fibre consists of the strict transforms of the two coordinate planes and the exceptional ${\mathbb{P}}^2$, all with multiplicity one. Its plane crossings make it singular; its closed ${\mathbb{P}}^2$ makes it nonaffine. The centre is deliberately on just one component of $xy=0$, keeping the fibre reduced.