[Arran]

Dave, try putting a few drops of wood glue on a business card  and slip it under the loose veneer and work it around a little. Use C-clamps and wood blocks on the front and back to clamp. Laminated counter top material makes good clamping blocks. The laminate will not become stuck to your veneer or you can use wax paper under your blocks.

Steve

Steve;
  One trick I figured out years ago is to wrap the blocks in either saran wrap or a plastic bag, glue doesn't stick to plastic bags nor saran wrap. Glue residue comes off with warm water and a brush. I was going to suggest a hypodermic needle and syringe to inject the glue, but not everybody knows where to get one, and it probably isn't necessary since the section that needs to be glued isn't that deep.
Regards
Arran