Bob Wild didn't say his tools rusted before they were in the chest, and they only rusted when in contact with the lining. This implies that the workshop is not damp and causing the rust.
These chests are available new, and so Bob may have bought a new one from Clarks. Michael's link shows that they are sold as tool chests.
So, if Bob bought it new, the first step should be to return it to Clarks as not fit for the purpose for which it was sold.
We are all practical types and try to find solutions to problems, but all too often this leads to us accepting unsatisfactory goods from suppliers.