Pocket watch J Lion and anchor marking

I have inherited a pocket watch with the following markings. Would somebody be able to give some more detail please?

The hallmark shows that the watch case is sterling silver and was assayed in Birmingham during the assay year 1858/59. A similar date letter J was used in 1933/34 but I am pretty sure that this is the earlier date. Unfortunately the maker’s mark, which would help to confirm the date is to worn and blurred in your picture to be recognisable.