I think I've solved the myster of Anne's mother now. My attention was drawn to Mary Owens (48) mother-in-law in the 1871 census entry found by Martin and her daughter, also Mary (13).
Hugh Jones Head M 24 Llanfaelog, Anglesey
Ann Jones Daughter F 3 Llanberis, Caernarvonshire
Mary Owens Mother-in-law F 48 Llanddyfnan, Anglesey
Mary Owens Daur of above F 13 Holyhead, Anglesey
After some searching I found them in the 1861 census back on Anglesey
Thomas Owens Head M 33 Llandyfrydog, Anglesey
Mary Owens Wife F 34 Llanddyfnan, Anglesey
Grace Owens Daughter F 10 Llangadwaladr, Anglesey
Mary Owens Daughter F 3 Holyhead, Anglesey
"England and Wales Census, 1861," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:M7GF-NW2 : accessed 8 June 2016), Grace Owens in household of Thomas Owens, Amlwch, Anglesey, Wales; from "1861 England, Scotland and Wales census," database and images, findmypast (
http://www.findmypast.com : n.d.); citing PRO RG 9, The National Archives, Kew, Surrey
Mary's age has gone crazy but apart from that everything matches. Note the 10 year old Grace. Here they are back in 1851:
Thomas Owens Head M 23 Llandyfrydog, Anglesey
Mary Owens Wife F 28 Llanddyfnan, Anglesey
Grace Owens Daughter F 5 MOS Llancadwaladr, Anglesey
Mary Morris Mother F 56 Llandyfrydog, Anglesey
John Williams Lodger M 22 Llanidan, Anglesey
"England and Wales Census, 1851," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:QKVB-FXSH : accessed 8 June 2016), Grace Owens in household of Thomas Owens, Holyhead, Anglesey, Wales; citing Holyhead, Anglesey, Wales, p. 16, from "1851 England, Scotland and Wales census," database and images, findmypast (
http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey
Mary's age is back to where it should be, and Grace is 5 months old indicating a birth in October 1850. There are no other children. So Grace Owens must be Hugh Jones's deceased wife. It struck me that his mother-in-law coming over from Anglesey (with daughter) suggested a recent death rather in childbirth and sure enough there's a death for a Grace Jones, age 20, in Carnarvon (which covers Llanberis):
Name Grace Jones
Event Type Death
Registration Quarter Jan-Feb-Mar
Registration Year 1871
Registration District Carnarvon
County Caernarvonshire
Event Place Carnarvon, Caernarvonshire, Wales
Age (available after 1866) 20
Birth Year (Estimated) 1851
Of course this means Grace was ridiculously young when Anne was born - just 17 - and it wasn't a surprise to discover that the marriage was actually slightly after her birth. I'd always believed that births outside wedlock were a huge deal in the 19th century but I've since found several Welsh ancestors who had a similarly "relaxed" attitude to getting round to marrying. As long as there was a clear intention to marry, and they did eventually do so, it doesn't seem to have been a big deal.
Anyway I believe the marriage was January 24th registered under "Bangor" which covers Anglesey. It look a little finding because it's been transcribed as Grace Owen but if you look at the image
http://www.wikitree.com/photo/jpg/Jones-41399 its clear Grace signs her name Owens. It means that Anne's birth was almost certainly registered as Anne Owens if you're looking for a birth certificate but there's so many it's a needle in a haystack.
The findmypast version nicely confirms the parents names too:
First name(s) HUGH
Last name JONES
Birth year -
Marriage year 1868
Marriage day 24
Marriage month Jan
Spouse's first name(s) GRACE
Spouse's last name OWEN
Parish BANGOR
Bride's first name(s) Grace
Bride's last name Owen
Bride's age Full
Bride's father's first name(s) Thomas
Bride's father's last name Owen
Groom's first name(s) Hugh
Groom's last name Jones
Groom's age Full
Groom's father's first name(s) Owen
Groom's father's last name Jones
So I believe that "Williams" is incorrect and that Grace Owens was Anne's mother. Perhaps Hugh remarried and Williams was her step-mother's maiden name? There are several possibilities for that.