"But as they were walking from the house towards the Orangery"
An Orangery
Creative Commons Attribution Share AlikeAn Orangery - Credit: Lincolnian (Brian)

An orangery is a building designed for keeping and growing plants – particularly fruit trees such as oranges.  Orangeries were typically attached to large homes built by the wealthy, and reached their peak of popularity in the eighteenth and nineteenth centuries. 

This suggests that Hailsham may be a former stately home given a new lease of life. A number of English stately homes have at various times been converted for use as schools, hospitals, rest homes and psychiatic institutions.