First of all, welcome to Rootschat!
Free BMD had Frederick John Nye born Oc/Nov/Dec 1850 and John Nye born Oc/Nov/Dec 1858, both Cuckfield.
HAve you ruled these two out? Census ages can be several years out!
Looking at it logically - if there is no John Nye born in Cuckfield in 1853/4, (and you have checked that out)then one aspect must be incorrect, so you need to work through them logically. Either it is the name, the date, or the place! (or more than one, in which case you are really stumped!)
So, starting with the date, you could investigate the ones I noted earlier.
by the way - Have you just looked on the free BMD data base? Or have you been through the full birth indexes quarter by quarter for these years?