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Emily's (Emmie) marriage register entry states that her father was Henry Hancock, farmer. Furthermore, there is this report on p.6 of the Saturday 2 July 1864 edition of the Western Gazette:

"[At Axbridge] Ann Jarvis of South Brent, summoned Henry Hancock, of Winscombe, to show cause why he should not contribute towards the maintenance of her illegitimate child. The magistrates, after a long hearing, considered the paternity proved, and made an order of 2s. 6d. per week and costs."

Which I think proves your theory on Emily's parents. I haven't looked at baptisms but perhaps Winscombe might be a possibility.

Best regards,
Richard

She was living with her grandparents George & Harriet Jarvis and her uncle Edmund in 1871 and in 1881 just her grandfather and uncle.

1891 she states she is a niece living with Edmund and states she was born at Biddisham, but there is no baptism there either.

I do not want to take the chance that there might be further info on a birth cert as that won't really help with a baptism.  I feel fairly confident that Harry/Henry Hancock is her father as he and Ann were god parents to my great grandmother Annie Jarvis baptised July 1863 aged 4.

Ann went on to marry in 1867 and then moved to Bristol leaving Emmie behind.

I think it might repay you to obtain a copy of Emily's birth certificate. According to Findmypast the mother's maiden name was Jarvis suggesting she was illegitimate. But the birth certificate might contain additional information.

Have you found Emily in the 1871 & 1881 censuses? Who was she living with?

Thanks for the suggestion Pat, but I have looked already as the family lived in East Brent in the early years.  The only baptisms I can find at the time of Emily's birth and a few years later are those of Ann's nieces and nephew,  her brother's children.

Ann's parents were George West Jarvis and Harriet Tilley and Ann was the youngest child born 1843. 

I have no proof that Ann is Emily's mother, it is just a guess but it could be that her only unmarried brother Edmund is the father and the mother is unknown although the maiden name on the GRO Index is blank suggesting it was Jarvis.

Perhaps I should go through all the PRs for the villages close by in case she was baptised away from the family home.  She was brought up by her grandparents working in the dairy until her marriage in 1897.