Should I replace a neighbour's bookcase after mistaking it for a free item at the kerb?

The bookcase was beside the other things my neighbour had labelled FREE. I carried it to my cousin's van.

Two hours later, my neighbour knocked and asked, “Have you seen a pine bookcase? The buyers are coming at six.”

The free label was taped to a box of mugs. There were also two dining chairs, which he did want to give away. The bookcase was a £40 sale, set outside so the buyers could load it easily. I had treated the whole little row as one giveaway and hadn't asked.

I called my cousin. She had already taken it to her flat forty minutes away and filled it with books. She will return it, but she can't borrow the van again until Saturday. The buyers have now cancelled because they needed it that evening.

I offered my neighbour £40 while we arrange the return. He wants the money and doesn't want the bookcase back; he says he shouldn't have to sell it twice. My cousin now thinks she should keep it if I pay, and I am in the middle of a sale that was never meant to involve me.

What is the cleanest offer to make? I accept that I should have checked. I just need us to agree what the payment and the returned furniture would each settle.