Hi,
Trouble with Shardlow Registration District is that it covers other counties apart from Derbyshire,
i.e. Nottinghamshire & Leicestershire.
Birth was registered Sept Q 1844, so by 1851 Census William would have been 6, a long shot
but there is:-
Clifford's Row, Long Eaton 1851 HO 107/2141 F 45 Pg 8
Parker John  Head M  29 Lace Maker          Long Eaton
"       Sarah   wife   M  25                            Lincoln
"     William   son         6   Scholar               Long Eaton
"     James    son          5     "                           "
"    Eliza        dau         5 months                     "
The only sure way is to purchase the Birth Registration Certificate.
Spendlove