Don't know as yet if it is your Ann Jenkins, but there was a report in May 1 1852 The Hereford Times p.7 re the illegitimate child of an Ann Jenkins - doesn't state the sex of the child or when the child was born, but that the order was made in August 1850 (so would have been born before that).
Abergavenny
Neglecting to support an illegitimate child
David Davies was brought up and charged by Ann Jenkins with neglecting to obey and order of Justices, made upon him for the support of her illegitimate child.
The guy I mentioned with the many name variations was listed as "John Jinkins Owens" on his 1939 Pennsylvania death certificate, which said he was born to Thomas Owens and Ann Jenkins of Danville PA in 1857. Through a very complicated series of documents I won't summarize here I can say with confidence "John Jinkins Owens" is another name for David Owens listed in the 1860 US census along with his dad Thomas Sr, his mom Ann, and his sibs John, Jane and Thomas Jr. I can also say with confidence he is buried under a gravestone with the name "DJ Jenkins."
Do you think the reason David changed his name has something to do with illegitimacy?