Hmmm. The reason I mentioned the varnish is that (apart from, IMHO, it looks awful!) is that it tends to crack, peel or wear off and it's quite difficult to match it piecemeal. I suspect the only way to get a uniform finish would be to strip the whole thing and start again, probably with a wax or oil finish.
But you might get away with the old antique dealers' furniture reviver - linseed oil, turpentine and vinegar, mixed up and rubbed on copiously, allowed to soak for an hour or so then rubbed off. If nothing else it smells nice!