On the 1871 census there is
George Simmonds 16 Croydon, Surrey, England Son Piddinghoe Sussex
Richard Simmonds 14 Croydon, Surrey, England Son Piddinghoe Sussex
Stephen Simmonds 52 Rodmell, Sussex, England Lodger Piddinghoe Sussex
This could also be your man found at
Piddinghoe, Sussex
RG10/1070 Folio 86
Also on the 1871 census from Rodmell (over 40 yrs old)
Isaac Simmons 16 Rodmell, Sussex, England Son Rottingdean Sussex
Matthews Simmons 19 Rodmell, Sussex, England Son Rottingdean Sussex
Sarah Simmons 57 Beddingham, Sussex, England Wife Rottingdean Sussex
Thomas Simmons 55 Rodmell, Sussex, England Head Rottingdean Sussex
Rottingdean, Sussex
RG10/1071 Folio 32
and also
Alfred Harriett 13 Hamsey, Sussex, England Son Tarring Sussex
George Harriett 16 Hamsey, Sussex, England Son Tarring Sussex
James Simmonds 44 Rodmell, Sussex, England Head Tarring Sussex
Mary A Simmonds 54 Barcombe, Sussex, England Wife Tarring Sussex
Tarring, Sussex
RG10/1070 Folio 80
Couldn't find anything else - nothing strangely on my IGI database. Perhaps check the British Vital Baptism Index and also the respect census and church records.
Please as they say always check what somewhat else gives you.
Regards
Keen