Thanks everyone for your interest and help.
We looked at all the possibilities for the marriage and the Mary ......... Wiot/Wiat/Wyatt was the only obvious one. There is a gap between the marriage and William's birth though. I'm wondering as Harting is so close to the Hampshire border, if other children's baptisms could be there? What does anyone think? They are definitely Harting people, but as they were agricultural workers they may have had to chase seasonal work.
Thanks Caroline for that site and I am certainly going to look into buying the CD. The Greentrees were originally Harting people and I think it would be an important part of their story.
When visiting in July I spoke to the Vicar and he said he had no known parishioners of that name now. He also said the records were at Chichester. In the Harting church they sold parchments scrolls of the Harting area, something I had not seen in other churches. I practically bought them out