Ordered certificates from the British General Records Office

[Spider Jerusalem]

1. Records were, generally, much less detailed until the mid to late 19th century

you're going to have a hard time finding a particular Mary Morgan in Wales, and I wouldn't expect that it'll be any easier if her father is called David--David is the patron saint of Wales; David or Daffyd is a very, very common Christian name in Wales and is the origin of the nickname "Taffy" for "Welshman".

If you know where your Mary Morgan was born then that may be of some help; the best place to look for parish record transcriptions is probably going to be familysearch.org--I've had good luck there, although parish records are very scarce or missing altogether in some places, and if your ancestors were nonconformists then there's much less chance of there being a record.

(Also, £9.25 per certificate? The UK isn't on the euro.)