Hi Joan
Can't find Elizabeth in 1851 census but there is a family living in Denbigh (Denby) in North Wales.
Residing at Swine Market, Denbigh
Rees Hughes 28 Skinner b. Dolgelley, Merionethshire
Abigail Hughes 30 wife b. Maentwrog, Merionethshire
William Hughes 5 b. Dolgelley
Jane Hughes 2 b. Denbigh.
This leaves a gap for Elizabeth who could have been staying elsewhere.
There are three Elizabeth Hughes in the BMD records for St. Asaph which was the place of registration for Denbigh.
Dec qtr 1847, Jun qtr 1848 and Sept qtr 1848. It is probably worth writing to the Superintendent Registrar at:
Register Office
Morfa Clwyd
Marsh Road
Rhyl
Denbighshire
LL18 2AF
for a copy of a birth certificate subject to a check on father's name.
regards, Fairlane