Thanks all for the advice. Went with a 38mm scaffold board, sanded all over, painted with two coats of clear preservative, and fixed into place with five 76mm screws into each post.
Along the river towpath near where I live a bench has lost its top, literally a plank nailed on to two wooden posts. I want to replace it as a bit of a gift to the community. This is not my strong suit - can I just use a brand new 38mm scaffold board (it's about the same dimensions as the plank...