I havn't found him on the census, I don't have an ancestry account. I do have information on the generation below.
Joseph Palmer (occupation on sons marriage certificate states, Gentleman) born 1811 in Leicestershire he married Caroline (possibly Leader) Abt 1806, Leicestershire.
They had Elizabeth (1827) Sarah (1829) John (1835) Caroline (1838) MAria (1840) and Joseph (1846).
My line follows through John Palmer the Census shows:
881
John Palmer...head...age 46...currier/courier??...brn Leicester
Elizabeth...wife...age 42..brn London
Henry W...son...age 20...currier/courier??..brn Northampton
Elizabeth..daur...age 19...hoisery...brn Leicester
Beatrice...daur..age 17...hoisery..brn Northampton
Emily..daur...age 15...hoisery..brn Northampton
John J...son..age 13...lace maker...brn Leicester
charles C..son..age 11..scholar...brn Leicester
Kate...daur..age 9..scholar..brn Leicester
Squires...son...age 6..scholar...brn Leicester
Ada...daur..age 3...brn Leicester
Thomas P..son..age 11 months..brn Leicester
They were living at 85 Bustall? St, Leicester, Leicestershire
Rg11, piece 3163, folio 34, page 9
1891
John Palmer...head...age 56..boot manufacturer...brn Leicester
Elizabeth...wife...age 53..brn London
Charles F..son...age 21...clerk...brn Leicester
Kate...daur..age 19...linker hosiery hand..brn Leicester
Stuires/Squires?...son..age 17...laster...brn Leicester
Ada..daur...age 13..warehouse girl...brn Leicester
Thomas C..son..age 10...scholar...brn Leicester
They were living at 35 Wand St, Leicester
RG12, Piece 2533, folio 143, page 20
1901
John Palmer...head...age 65...currier (leather)...brn Leicester
Elizabeth Palmer...wife...age 62..brn London
Beatrice Gent...daur (married)...age 36..hosiery winder..brn Northampton
Squire Palmer..son..age 25..shoe hand/ heel maker ...brn Leicester
Thomas Palmer...son..age 20..shoe hand/ getter off..brn Leicester
Beatrice Gent..grand daur..age 8...brn Great Pearley, Leicestershire
Living at 6 Crafton St, Leicester
Rg13, Piece 2992, folio 31, page 1
Not sure of a Sydney Palmer?