Her Mother's name will be on her birth certificate - saves speculation as to parentage.
Interesting, also registered on the same page:
Births Jun 1850
Purcell Joseph Dudley 18 267
Purcell Mary Dudley 18 267
No marriages showing in Dudley from 1850 to 1851 for any Purcells.
Added:
There is a death for a Joseph Purcell in Dudley later that year, which could be him as no ages recorded in 1850.