Unfortunately the occasional flood and general cold and damp during the winters are not doing it any good. I decided I either needed to sell it or move it in to the house before it deteriorates beyond a reasonable chance of repair.
The repair has gone reasonably well so far. I've started with the drawers. Each has been re-glued where joints appeared weak or were separating. Only a couple needed major surgery and only one needed to be completely taken apart and re-joined.
The handles are all rusting to various degrees. I did try sanding off the rust with the plan to lacquer them but the results were disappointing. I have painted them black instead.
I am not aiming for anything historically accurate. This furniture was common in shops. Made to look good from the front but of generally low cost construction. I want to end up with a piece of furniture that will be usable for many more years.
All the drawers are now together and I have waxed them so they have a nicer finish.
Some of the drawer bases may need to be replaced in the future. All the plywood felt flimsy plus some of the layers on some drawers had separated, probably due to damp. I have glued these layers back and they appear to be stable. Only time will tell how well the bases will hold.
The next job will be to repair the frame. The front is in good condition but the lowest edge of the old chipboard sides, where they have stood in the damp, are crumbling and will need some fixing and additional support.