The Mouseman workshop in Kilburn, North Yorkshire, is still run by the family of Thompson, who died in 1955.
The tables date from 1935 and 1937 and are expected to fetch up to £20,000. The four benches are being sold as separate lots.
The 1935 table is 5m long and estimated to attract bids of £5,000 to £8,000, while the 6m-long 1937 table could go for £8,000 to £12,000.
The longer table features a brass plaque with the engraved words: “Presented by a grateful old boy who went from Moorlands to Shrewsbury and Corpus Christi College, Cambridge.”
Ms Atkinson said the school had a strong community of alumni, many of whom had been in touch on hearing that it was set to close.
She said: “We regularly used to get phone calls from old Moorlanders asking if they could come and have a look around the school building because people just had very fond memories of the school. It’s very strong kind of sense of community here.
“It’s been difficult because we had hopes that we could have opened the building up (for final visits), but things have moved on quickly that we just felt it wasn’t kind of appropriate in the end.”