The report said the departments of health, justice, defence, local government and education need to use gardening to cut childhood obesity, improve public spaces, help mental health and rehabilitate prisoners.
The network is an independent organisation which voices "decentralised, growth-orienatated solutions to environment and resource issues". Supporters include Greg Barker, Zac Goldsmith MP and Nick Hurd MP.
Conservative MP Rebecca Pow, the All-Party Gardening and Horticulture Group secretary, wrote in the report: "Gardens, gardening, and horticultural skills can have a striking effect on our communities.
"Getting more people gardening is a truly holistic, cross departmental, high impact policy.
"Having spent much of my career pre-politics involved in garden journalism and broadcasting and working ‘in the field’, I am acutely aware of the rich benefits society can gain from horticulture, touching as it does on urban regeneration, growing food, contributing to the economy, influencing our well-being and surrounding us with beauty.
"These green gems provide important outdoor playgrounds for relaxation and exercise, often offering a therapeutic alternative to the pressures of everyday life.
"Realising the free benefits the outdoors can offer, some GPs are recommending ‘green prescriptions’.
"The garden economy makes a significant contribution to the nations’ coffers, with £7.8billion being spent on this sector by tourists every year.
"Parks and gardens are valuable habitats for wildlife and nature, capturing and storing carbon helping to combat climate change and reducing flooding.
"A bit of healthy rivalry for the best front and back gardens encouraged the clearing of litter, (now there are regular community litter picks), the cutting of verges and of course the growing of a kaleidoscope of colourful ornamental plants and some nutritious vegetables.
"The physical effect on the area of having pretty gardens was significant but the competition also engendered a great community spirit, getting people out talking over garden gates.
"From tiny acorns, mighty oaks will grow. Certainly, providing people with the opportunity to green their communities can be a way of tackling deprivation – unemployment, lack of skills, low education attainment and mental health.
"Government departments are all working on individual responsibilities as they relate to deprived communities; the Home Office on drugs and crime; the Department of Health on mental health; Department for Work and Pensions and the Department of Communities and Local Government on unemployment and of course Defra on horticulture.
"To get the full benefits that the power of plants can provide our communities with, especially in urban areas, requires an interlinked approach and now is the time to sow those seeds and spread those roots for the greater good."
Prime Minister Theresa May said the report "raised the health benefits of green space, which are becoming ever more recognised".
Defra "will consider the evidence within that report and will focus on what can be done to ensure that the benefits provided by access to green space are available to all segments of society" as part of its 25-year environment strategy.
Report contributors are Pow, Richard Bacon MP, Victoria Prentis MP, Helen Whately MP, Dr Matthew Offord MP, Andrew Selous MP, Alex Chalk MP, Neil Parish MP, Jo Churchill MP, Richard Benyon MP, and CEN’s Interim Director Mark Holmes.