Thanks very much Julia,
It looks like WALKER was the real surname - I've found a baptism for Ann WALKER (parents Joseph and Harriet on 23 Nov 1834 at Burnham on IGI (Batch No. C013598). The fact that Harriet was born in Stroud was just a tantalising coincidence. Thats one possibility firmly eliminated.
I'm still not convinced that Joseph was born in Stroud - The 1841 Census states that he was not born in the county, but Harriet and the children were. There is some debate over wether Bristol was in Somerset or Gloucestershire, but if father and children were all born in the same town, the answer to the question of were they born in this county should have been unanimous - either all yes, or all no.
Sandra