Basham, who is based in Greenwich Park and works for landscape maintenance provider Turfsoil, was judged to be the person who has most benefited from her first year on the three-year Royal Parks Apprenticeship Programme, which was relaunched in 2007.
Chairman of the Royal Parks Guild Mike Fitt said: "Zoe has been an outstanding apprentice and after just one year she has reached a high standard of competence and practical ability."
Turfsoil chairman John Newton said: "We are delighted that Zoe has won this most prestigious award. She has been a model employee and fully justified the ongoing support that Turfsoil has been pleased to provide to the Royal Parks' apprenticeship scheme."
Basham said: "This was a complete shock and I'm delighted."
The Royal Parks Apprenticeship Programme aims to recruit 10 new apprentices each year.