If you're looking for work specifically with trees click here to the Arboriculture section.
Typical jobs include Gardener, Wildlife Gardener, Horticultural Manager, Community Allotment Project Officer, Horticultural Therapist. the National Careers Service has role profiles for some of these and many more (click the links)
Farm work often includes working in close contact with animals, in the countryside sector this could include Conservation Grazing projects. The National Careers Service profiles a Farm Worker.
See current vacancies advertised with CJS here.
There are many different skills and qualifications required to work in horticulture
If you're thinking of a career working in horticulture there are details of longer courses such as practical horticulture skills and garden management on the Training Directory here.
Some courses are available by Distance Learning such as RHS Certificate in Principles of Horticulture, see these here.
Creating and restoring new habitat or accidently spreading plant pests and pathogens?, The James Hutton Institute
How to set up a community garden, Social Farms & Gardens
Horticulture careers with the National Trust: 500 years of garden history, a lifetime of opportunities, National Trust
The power of community gardens – growing people and places, Groundwork
How productive gardening can help wildlife (and measures large scale producers are taking), Wildlife Gardening Forum
From Opera Singer to Heritage Horticulturist….., RHS
The orchard habitat, PTES
Creating a wildflower garden, Plantlife (Featured Charity 2017)