Hi,
There is a Beatrice May Parry born June 1893 Pontypool 11a 156 on FreeBMD. She is the only Beatrice May Parry born in Pontypool so she must be yours. If you send for the birth certificate it will give her father's name and occupation as well as her mother's Christian name and maiden name. Armed with this information you can then begin following the families back through the censuses, as well as looking for her parent's marriage. Their marriage certificate will give the name of her grandfathers and their occupations.
Hope this helps.
Emeltee