On the 1881 census, with parents Caleb and Emma, Elizabeth's birth place is shown as Clyffe Pypard and on the 1891 census, (after her marriage) her birthplace is given as Thornhill. Clyffe Pypard and Thornhill are about 2 miles apart, so either place is probably correct. even today they are very tiny places near Wootton Bassett and about 10-12 from Leigh. Edward on the 1891 census is shown as born at Hilmarton, as does the 1901 census. It is about 6 miles from Hilmarton to Thornhill.
If Caleb is their father, he was an agricultural labourer and would have gone to whichever village had work, and it's always possible that his wife went with him so that the children were born in different villages. In fact looking at the 1881 census, the first two children were born in Clyffe Pypard and the others in Hilmarton.
To summarise:
1. Why do you say Elizabeth was born at Leigh, when the census shows she was born at Thornhill, which came under Cricklade registration at the time of her birth. Do you have her birth certificate?
2. There is a birth of an Edward Gough, born in 1884 (which ties in with the census entries. The registration area in his case is Chippenham, which covers Hilmarton, Edward's birth place on the 1891 and 1901 census.
3. If you don't have Elizabeth and Edward's birth certificates it might be worth buying them, that would show who their parents were.
4. If you don't have their marriage certificates, you could buy those if you prefer, but these would only give the father's name.
Lizzie