Are you local Mr. Snodgrass?The wood looks like antique faded mahogany, a photo of the whole piece would help though. The marks are caused by iron being in contact and reacting with the tannin in the wood. you will have to take the finish off, if it is antique it should be shellac and should come off easily with meths and fine wire wool. You will then need to bleach out the stains with oxalic acid then refinish.
https://apcpure.com/product/oxalic-...box-friendly-pouch/?attribute_pack-size=100gmor
liberon oxalic acid
You may be able to get either one of these from Handyman in Tewkesbury.
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