If the shallow buttons will work for you, that's probably the way to go, but if you do decide to fill it in, Bondo works wonders! Not sure if this would have the same name in the UK or not, but it's basically autobody filler. When it dries, it's as hard as the wood. If you do a good job of sanding it and covering it, no one will ever know there were holes there. I would strongly advise you to do it outside though, as the fumes off that stuff are nasty.