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I may be wrong
But the legs of each of the chairs are held to the chair frame by pegs which I was able to separate with a rubber mallet as they were all lose. I assume the table les are attached the same way.

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Don't !
This table base is unique, in that the corner block is apparently glued to the apron members -- which in turn locks the legs in place via the dowels.
You won't free the legs unless you a) magically unglue the block from one apron, or b) magically remove the dowels while the legs are still in place.
Impossible ? Yes. Therefore, the solution is to introduce long screws through the free face of the corner block into the leg. Do one at top and one at the bottom of the block, and have them penetrate 2/3 of the leg diameter (at least).
Amateur advice is quite troubling, at times . . . !

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The dowels
go from the leg straight through where the two sections of the apron meet into the corner block. The dowels are not of the leg or of the block. There will most likely be three dowels per leg.
You will break a bowel or two, it is not a big deal, just drill out the broken bit (dont enlarge the hole) and use a new dowel to make the repair.
This is the proper way to do it, or pay somone with with experience to do it this way. Screws are a hack repair, not original construction and will devalue your piece.

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BRAVO
you posted the seperation pic as I was responding. Nice work.

Breaking dowels
If you do happen to break a dowel one trick to drilling out the hole is to drill a smaller (than the dowel) hole in the middle of the dowel and the break the dowel into pieces into the hole in the middle. Then you can clean the hole of glue chunks and remaining bits of dowel with a quick spin with a drill bit of the correct size.