The box on the RHS is indeed for watch/clock lathe work (mine has a plate showing "Boley" on the lid).
Can't recognise the item on the bench RHS but from your description "chrome item on left (??)…2 brass wheels etc…." I'm not sure it's clock related.
There's an old hand-held small vice missing its wingnut (replaced by crude nut & bolt).
Next, an Archimedean drill.
Last on left is a hand-held tool for tiny collets.
The wooden box on the left appears to contain hand tools for cutting 'cups' on clock plates where wheel arbours emerge (cups cut for oiling and reducing length of brass for arbour once broached.
They're all pretty much interesting antique items and if your offer to pass them on isn't taken up, such items often appear on Fleabay .