Removing the back panel is a difficult job, but that's what you might have to do here. You can take the removed panel to Bunnings etc and they should have the correct replacement and cut it for you. You will have to route the bottom section. While you have the cabinet apart, replace the bottom section as well.
If you want to replace the bottom panel, Bunnings may not have the correct thickness masonite.
I ended up using braceboard, it's still masonite, it's 1/4 inch (6.35mm) thick which is what was required for the Williams cabinet I repaired.
To help the strength of the cabinet you could also glue the masonite in and nail it in too, just make sure the nails will be hidden by the cabinet side repair strip.
