That baptism looks like a good bet since parents James and Alice are in Southwark in the 1841 and 1851 censuses:
1841 census: Worcester St, St Savior, Southwark, Surrey (HO107/1088, book 4, f 17, p 26)
James Arnold, 39, Hatter, N
Alice Arnold, 38, N
Ann Arnold, 14, Y
Letsy Arnold, 11, Y
William Arnold, 8, Y
George Arnold, 2, Y
1851 census: 5 Grove, St Saviour, Southwark, Surrey (HO107/1558, f 423, p 82)
James Arnold, Head, Mar, 49, Hatter, Derbyshire
Alice Arnold, Wife, Mar, 48, Nottingshamshire
William Arnold, Son, U, 17, Hatter's Apprentice, Southwark
George Arnold, Son, 11, Southwark
Alexander