cast iron garden bench

We normally call that 'racking'.

To minimise racking, yes.

Ensure the slats are attached to the ends as tight as possible (without crushing the wood etc) and if that isn't sufficient, add some (two) diagonals across the back (could be wires or flat steel straps) to further restrict said racking.

Even one diagonal would help.

Cheers, T i m

Unless there's some diagonal bracing, it's quite optimistic to hope the wooden slats alone will stop it rocking.

What is needed is new slats that completely fill the holes in the sides. Given that the slats have already been cut to size, it might be worth cutting a few wedges and hammering those in to fill up the gaps. If there's any movement, they'll probably tend to work themselves loose. At least, it will enable you to see how rigid you can make it just with the slats before going to the trouble and expense of getting new ones.

An example of braces (and a strap which also adds rigidity) is here

Always worth looking for parts left over from the old one :)

Cheap slatted benches with metal ends, available in many retail sheds, seem to only need the central metal strap to keep the bench rigid.

I suppose that is because in order for the metal ends to go "off vertical" the slats all have to become misaligned. And the strap goes a bit of the way towards making the slats more like a solid sheet, with shear strength. Slightly surprising, but if it works...

Tighten the end bolts, not excessively. Add bracing if necessary. Benches vary a lot in their stability in original form.

NT