In light of those names there is this family. Which could of course be just co-incidental
1871 census
3 Cold Bath Square, St James, Clerkenwell
Naomi Batchelder head widow 52. Waistcoat maker born Southend Essex
Elizabeth N. Batchelder 21 daughter, b London, Middlesex
Frederick Batchelder 19, son, porter. b Willesden, Middlesex
Arthur Batchelder 17, son, compositor, b Southwark, Surrey
Willliam Batchelder, 15, son, Warehouse worker, b Southwark, Surrey
Births that fit that census are
BATCHELOR, Elizabeth Neaoma. MMN WARREN. 1850, March, Marylebone, vol 01. page 215
BATCHELDER Frederick John, MMN WARREN 1851 D qtr, Hendon, vol 03 , page 272
BATCHELDER Asher MMN WARREN. 1853, D qtr, St Saviour, vol 01D, page 22. **
BATCHELDER William James MMN WARREN. 1855 D qtr St Saviour Vol 01D page 4
Is Asher = Arthur?
so a marriage that fits is
James BATCHELDER
Naomi WARREN. St Geo Han Sq 1/33/Dec 1850
5 December 1850,
James Batchelder, full age, bachelor, servant, Grosvenor Street, father James Batchelder, Farmer
Naomi Warren, full age, spinster, Grosvenor Street, father William Warren, Gardener
All sign
Witnesses Charles Walden and Elizabeth Warren
1881
28 Gloucester St, St George Martyr
Naomi Batchelder 62, Mother, Waistcoat maker, born Prittlewell, Essex
Elizabeth 30 , waistcoat maker b Marylebone, Middx.
Possible death for Naomi 1889 age 74. St Giles, vol 01B page 317