Hi Lavender123,
Well so far, I do think there is a fair to great chance, the Frederick SIMMON(D)S, father and son, found in 1871 Census I posted above, is your fellow. That family ended up in West Ham, Essex - where your Frederick was with his wife Mary Ann in 1901 and beyond.
The son Frederick in 1871 is the right age and place of birth (b 1870, b Gravesend), and right father's name (Frederick) - to match your Frederick b abt 1870 in Gravesend as per details his 1901 Census and 1896 marriage.
The father Frederick (b abt 1838) in the Census all the way through, is consistently a 'Labourer' or 'General Labourer'. However, that's a very common sort of occupation to be 'talked down' on Census whereas he could actually have been a 'Foreman' of a group of labourers, or conversely, a General Labourer could be talked up on a Marriage Cert, not uncommon either. I wouldn't discount this family due to that occupation 'discrepancy', anyway. Here are the details (you'll see the surname is either recorded with or without the 'D'):
1861: Chapel Street, Village of Coseley, Sedgley, Staffordshire
Head: Frederick SIMMONS 23, Gen Lab, bWest Ilsley, Berkshire
Wife: Sarah SIMMONS 24, b Darlaston, Staffs
Dau: Mary SIMMONS 11, b Sedgley, Staffs ( this likely meant to be 11mths, or 1 month, or 11 days, etc)
1871: At 8 Terrace Court, Gravesend
RG10 Piece 890 / Folio 45 / Pg 22
Head: Fredrick SIMMONS 33, Labourer, b Ilsley Berkshire
Wife: Sarah SIMMONS 34, b Darlaston, Staffordshire
Dau: Mary SIMMONS 10, Walbrook, Staffordshire,
Dau: Sarah Ann SIMMONS 7, Pensnett, Staffordshire,
Dau: Julia SIMMONS 5, b Battersea Park, Surrey
Dau: Elizabeth SIMMONS 3, b Battersea Park, Surrey
Son: Frederick SIMMONS 5 mths, b Gravesend Kent
1881: At 43 Benges Street, Canning Town, West Ham, Essex
RG11 - Piece - 1716 - Folio 15 - Pg 23
Head: Fredrick SIMMONDS 43, Gen Labourer, b West Ilsley Berkshire
Wife: Sarah SIMMONDS 43, b Darlaston, Staffordshire
Dau: Julia SIMMONDS 15, b Battersea, Surrey
Dau: Elizabeth SIMMONDS 13, b Battersea, Surrey
Dau: Frederick SIMMONDS 10, b Gravesend Kent
Dau: Ellen SIMMONDS 7, b Shornward, Kent
Dau: Edith SIMMONDS 1 mo, b Canning Town, Essex
1891: At 42 Benges Street, Canning Town, West Ham, Essex
RG12 - Piece 1318 - Folio 133 - Pg21
Head: Frederick SIMMONDS 53, Labourer, b Iisley, Berks
Wife: Sarah SIMMONDS 54, Laundress, b Darlaston, Staffordshire
Dau: Elizabeth SIMMONDS 23, unm, Laundress, b Battersea, London
Son: Frederick SIMMONDS 20, unm, b Gravesend, Kent
Dau: Edith SIMMONDS 10, Scholar, b West Ham Essex
1901 At 43 Benges Street, Canning Town, West Ham, Essex
RG13 - Piece 1581 - Folio: 164 - Pg 63
Head: Frederick SIMMONS 63, General Labourer, b West Ilsley, Berks
Dau: Elizabeth SIMMONS 33, unm, Laundress, b Battersea, London
Dau: Ellen SIMMONS 27, unm, Laundress, b Shorn Kent
Dau: Edith SIMMONS 10, Scholar, b West Ham Essex
Grandchild: Lily WHITTING 14, b West Ham, Essex
Cheers
AMBLY