Was Shakespeare a chronicler of climate-change disaster? A Midsummer Night’s Dream presents nature in crisis, brought about by the disruptions of the fairy and human worlds. In Joe Hill-Gibbins’ glumly dark revival at the Young Vic this year, the stage was covered in mud, suggesting not only how relationships get bogged down but also a sliding-away world of rotting crops and drowned fields. As Titania proposes, it is down to us to acknowledge responsibility for this “progeny of evils”. But isn’t it odd that what is seen by many as one of the greatest challenges of our time receives so little theatrical attention, particularly in the mainstream?

Katie Mitchell has vowed to make one work a year that addresses environmental issues; at the Royal Court, her collaborations with scientists in the dramatised lectures Ten Billion and 2071 presented the world that our children – and theirs – will inherit. This year the remarkable Slung Low have produced a three-part epic, Flood, in Hull, which is the 2017 city of culture and could also be one of the first UK cities to be drowned as sea levels rise.

Maybe it is hard to make audiences face the facts when theatre companies can be part of the problem. Buildings gobble resources and touring makes a carbon footprint. The carbon-neutral Arcola in east London is still the exception rather than the rule. Earlier this year, the Royal Shakespeare Company staged a double bill, Myth and Earthworks, that pointed the finger at personal and governmental inaction. In Myth, written by Kirsty Housley, a dinner party turns bad as dead birds flop from the ceiling and oil runs down the walls. But why should we take this warning seriously when the RSC continues to take sponsorship from BP?

In a 12-day festival in London, Shoot the Breeze, Camden People’s theatre is addressing global warming, pollution and the environment. The lineup has included a laid-back, cabaret-style entertainment entitled FFS!! by Timberlina, “the bearded drag lady who gives a shit”, which gently sends up eco-anxiety. The show teases rather than preaches as Timberlina satirises middle-class and hipster concerns around upcycling and wood-burning stoves. Anxiety was also the theme of Louise White’s work in progress The Dead Sea, an image-rich show about a marine biologist who is investigating the effects of plastic in the oceans on the food chain, and has become scared of the sea. The Dead Sea will tour the east Midlands early next year, by which time its metaphor about how fear paralyses and stops us changing the future should be a keener one.

Sending up eco-anxiety … Timberlina in FFS!! Photograph: Eoin Norton

Later on at Shoot the Breeze, the all-female theatre ensemble Urban Foxes Collective will consider the ethics of reproduction in an overpopulated world in their show Floods. The festival’s centrepiece production is Fog Everywhere, directed by Guardian journalist Brian Logan, made in collaboration with local teenagers and with scientific input from the Lung Biology Group at King’s College London. In the show, a group of young people consider their future as they try to breathe in a city that this year had breached its targeted annual limit on air pollution by 5 January. As in The Dead Sea, mental health is an issue: could pollution be a factor in the panic attacks one girl graphically describes?

This is a show about personal responsibility that looks back to the smog of the Victorian era and, in particular, Robert Louis Stevenson’s descriptions of it in The Strange Case of Dr Jekyll and Mr Hyde. But it also has its eye on the future. The young people describe their own lives and the way they want to be living in 2040 when they will be approaching the age of 40. Most of them don’t want to raise children in London.

There are balloon-blowing competitions, personal revelations, an attempt to sell us canned air and lots of irreverent teenage wit. Great play is made of grime music and the griminess of the city. The show constantly balances the perks of living in a city with the perils, including its unseen pollution. During the work’s 65-minute duration, the roar of traffic on Hampstead Road can be clearly heard inside the theatre.

At one point, a teenager holds a torch up in the dark, trying to show us what cannot be seen: the invisible particles that poison the air. Maybe we haven’t progressed as far as we like to think from the dirty air of Victorian London: more than 9,000 Londoners die each year from pollution. These youngsters make you think about every breath you take.

• Fog Everywhere and Shoot the Breeze festival continue at Camden People’s theatre, London, until 11 November. Box office: 020-7419 4841.