As suggested by wazkelly I have sanded off the rest of the veneer.
Funny how you can sand through it so easily then it takes ages to get the rest of it off :-)

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So it is very, very plain which would be great for a solid finish.
But I had my mind set on a stain so decided I am up for the challenge to do a new veneer so the binding has been removed.
There's quite a bit of stubborn glue left to deal with but we're getting there.