According to the one English Census that James O'Brien has been found in (dated 1861), he was born around 1810, in Ireland. At that time he lived at 5 Marsh Street, in the centre of Bristol, England. He was 50 years old, and was married to Catherine (nee Mahoney). They had 2 children living with them (Patrick and Michael). He worked as a Linen Weaver. In the same building there was another man called O'Brien. His name was Cornelius and he was said to be aged 60. He was said to be from St Mary's, Cork, Ireland. James died, in Bristol, in the last Quarter of 1868 (according to the Death Registrar Records). In the 1861 Census both James and Catherine were said to be from Ireland... without any more details.
We got Catherine's Maiden Name from the Baptismal Details for their son, Michael, who was Baptised at the local Catholic Church in the centre of Bristol (St Mary's on the Quay) in March 1855. Catherine also appears in the 1871 Census. She still lived in Marsh Street, Bristol. She was said to be Cork, Ireland... so this gave somewhat more detailed indication as to where she was born.
The O'Briens were on my Mum's side of the family. Her mother was Joanna O'Brien (the Grand-daughter of James and Catherine). We were told that the O'Briens were from Cork.
It's not clear when James and Catherine arrived into Bristol. They don't obviously appear on any earlier Censuses.
The reason why I think that James was from St Mary's is because of the fact that, in 1861, a man called Cornelius O'Brien (who was from Cork, St Marys) lived in the same tenement as James.
Using this "potential" connection, I found that a James O'Brien and a Cornelius O'Brien (both of around the correct ages, based upon the limited data from English Censuses) were born to Charles O'Brien and Margaret White... and both were baptised at St Mary's, Cork.