The coachroof and the deck of an Atalanta are made made from three layers of 2.5mm thick agba veneer, each layer layed at 90 degrees to the one below. So it isnt plywood, as such.
To make a proper repair is actually quite easy, when you go about it in the proper way which is described in one of the original Fairey marine drawings. Lots of people seem to want to find a shortcut – but perhaps it is easiest if I describe how to do it properly.
Firstly I would start on the inside. Look at the actual hole. That is the size of the patch you will need to fit into the MIDDLE layer. It is probably easiest if you sand or scrape the paint off around the hole so that you can see which way the grain is running in the lowest (inside) veneer. Now draw a pencil line in a diamond shape about 1/2″ to 1″ bigger all round, making the diamond shape longer in the direction that the grane is going. Hold a metal rule against the line and cut along it with a stanley knife. You MUST use a new blade. Press gently at first and go over the line pressing a bit harder each time until the blade has cut down about 2mm. Now use a sharp chissel to carefully cut out the diamond. You will see the glue line as you cut it away so you will now when to stop cutting deeper. You can cut around the actual hole to make a square or regular shape for the hole in the middle layer.
Cut a piece of paper large enough to go over the diamond shaped hole and press it firmly into the edges, taking care to make sure it does not move. You can draw around the edges with a pencil, but I just crease the paper into the edge of the cutout pressing firmly with my nail.
Cut out the diamond shape from the paper and try it in the hole – it should be a good fit with no gaps. When you are satisfied with the pattern, hold it onto a piece of veneer, and using a metal rule cut it out in the same way as I described cutting the deck. The resulting diamond shaped patch should be a good fit into the hole.
A second similar piece of veneer can be cut out slightly smaller to use to make the patch for the middle layer. Hold it in place temporarily with a couple of staples from the inside, while you draw around it from the outside to get the shape of the hole in the middle layer. Cut that patch out. You can now fit these two patches permanently. Most of us use West epoxy, for this type of repair. It is less temperamental than most epoxy systems. Whatever glue you use it does need to be waterproof and structural. If you use an epoxy (which I recommend) you will need to mix filler powder into the mixed resin and hardener, until it is the consistancy of peanut butter. Fit the inner layer and staple it in place, then fit the middle layer patch from outside.
You can leave the epoxy to set and deal with the outer layer the next day.
How far should you cut back the outer layer?
If you want a professional repair in a varnished surface you have to cut the outer veneer back along the grain each way until you meet an obstruction. Also it has to be as wide as the original veneer. The idea is to leave the finished surface with no extra joins.
In practice if you accept that the edges of the parch will be visible or it the surface is painted than cut out a patch just like that in the inner layer, using the same techniques, and glue it in place.
The repairs can be sanded after 24 hours, and you should hardly be able to see the edges.
If you let me know how big the hole is (small I presume?) I can bring some agba veneer to Doggets for you.
For reference Robbins Timber of Bristol stock Agba veneer.
Dont worry about UV resistance which will be provided by the paint or varnish you apply over the patch.