Extra to spendloves info;
Also bapt to Matthew/Mary;
JANE Diddle 16 May 1819
ELIZABETH Didwell 05 Feb 1822
1841 Census is no help for Matthew as you say he is is living alone age 60 (1781) in St Peter Walpole.
Maybe Jane?
Marriage;
02 Jun 1846, St Mary Magdalene, Fleet, Lincolnshire*
George HALLIFAX, Bachelor, Sull Age, Fatmer, Father EDMUND a Farmer
Jane DIDWELL, Spinster, Full Age, Servant, Father MATTHEW a Labourer
Witnesses, Sarah HERBERT/John JEALOUS
1851 Census Jane Hallifax is born c 1821 Warpole, Norfolk
She died 1898 in the US
Elizabeth also may have married Lincolnshire 08 Dec 1845 Moulton to James BATEMAN
Details on Father are the same.
All above on FreeREG
EDIT looks like her;
1871 as Elizabeth Bateman 1821 Wapel Norfolk, living in Lancashire
1861 as Elizebeth Bateman 1820 Nawfork, living in Yorkshire
1851 she is in Hunts with her Husband (where he was born) her pob dittoed from his.