The parents of John Wildgose were Sir Anthony Wildgoos and Margaret Lennard. Resided at Edridge Court, Sussex. John and Grace had a son Annesley (Anselm), who was knighted 22/5/1605. His son was Robert Wildgoose born 1615 and knighted 1/2/1640.
The Lennards can be traced back through the Fiennes, Nevilles, Staffords, Percys, Woodvilles to the Tudors. I have not had any luck yet with Wildgoose.