Hi
On the 1851 census Elizabeth gives her birthplace as Northampton.
Elizabeth is not with her husband at Preston Hall Lodge Aylesford on the 1861 census, she is at Preston Hall Mansion Aylesford
RG9 484 folio 10
Elizabeth Burford 50 Servant Married Cook Wilbarston Northamptonshire
Thomas was a widower by the time of the 1871 census.
Why would Elizabeth give her birthplace as Northamptonshire on two separate censuses if she really came from Kent? Wilbarston and Brixworth are about 13 miles apart. Have you checked for potential Elizabeth Green baptisms in Wilbarston?
Since Charles Annis (Marsahll) Green was the illegitimate son of Elizabeth Green, his father is unlikely to share the surname Green, though undoubtedly with a reasonably common name like Thomas Green the Royal College of Surgeons is likely to have surgeons in their lists called Thomas Green. The Annis Marshall combination of his name on his baptism is more likely to point at least in part to the name of his father, but censuses show Annis Marshalls were all female living in the north of England so it isn't just a straightforward lift of a potential father's name.
Regards
Valda