Hello Richard, There is a record in Burke's general Armory of arms granted to Edward Prest Esq. of the city of York in 1823. The arms are: Per bend sinister erminoise and sable, on a fess cotised between three martlets two mullets all counterchanged. The crest is given as A semi terrestrial globe proper thereon a demi pegasus regardant ermine semee of mullets gules supporting an anchor erect sable.

If you can prove that you are directly descended from this gentleman in the male line then you have a genuine claim to the arms. If you aren't descended from him then you would have no claim to them.

regards,
Martin
http://cheshire-heraldry.org.uk