HI Dee-Jay - as per your suggestions I contacted the two agencies and, as it turns out, the HeritageAdmin folks sent my request to the WSHC one anyway...
Turns out all your sleuthing resulted in the best accuracy about the records they do hold, this is what they told me "We hold the parish records for Wiltshire. There are baptism and marriage records for Chittoe from 1846 but no burials, these would take place in Bromham".
They also provided some additional names, which I have to clarify, but it looks like there were 4 or 5 siblings for my relative (not the two I had records for).
I will go to the WSHC whilst in Wilts and look at the birth marriage records. I assume Bromham has a similar facility?
Thanks so much everyone for all your input and efforts!! I am so happy with the progress you all helped me make in just a couple of days. Regards, Carol