https://www.thelancet.com/journals/lanplh/article/PIIS2542-5...

The study, linked to from the article.

This is only the most recent of many studies into this, eg. https://pmc.ncbi.nlm.nih.gov/articles/PMC5663018/

> There is an urgent global need for accessible and cost-effective pro-mental health infrastructure. Public green spaces were officially designated in the 19th century, informed by a belief that they might provide health benefits. We outline modern research evidence that greenspace can play a pivotal role in population-level mental health.

> Findings A total of 129 335 adults were included in the final sample. In the cross-sectional, between-individual analysis, we observed a greater risk (adjusted odds ratio [aOR] 1·10 [95% CI 1·03–1·20] p<0·05) of antidepressant prescription for those living within 800 m (approximately 10-min walk) of an improved woodland compared with those living further away, but no significant difference in the risk of anxiolytic prescription. In the longitudinal, within-individual analysis, we observed lower prescription use for antidepressants (aOR 0·90 [95% CI 0·87–0·93] p<0·01) and anxiolytics (aOR 0·94 [0·90–0·99] p<0·01) during periods spent living within 800 m of an improved woodland when compared with periods spent living beyond 800 m of an improved woodland.