Pinned just west of Marsden, Yorkshire on a 17th-century map of the UK, is a poem by the UK’s new poet laureate, Simon Armitage. “The sky has delivered / its blank missive. / The moor in coma.” Move west, to the Isle of Man, and the poet is a little less well known – she’s dubbed herself Mrs Yorkshire the Baking Bard – but the sense of place is just as strong (and the rhymes are better, too): “I climbed Maughold Head as the morning sun rose / And the darkness surrendered to light / Where the buttery bloom of the golden gorse grows / And adventurous seabirds take flight.”

The poems – two of almost 2,000, and growing – are part of the Places of Poetry project, a community arts initiative where members of the public are invited to write poems and “pin” them on a digital map to the locations in England and Wales that inspired them. Inspired by Michael Drayton’s 17th-century poem Poly-Olbion, a 15,000-word poem on the topography of England and Wales, the project is being run by poet Paul Farley and Andrew McRae from the University of Exeter.

McRae calls Poly-Olbion an “extraordinary, unique and slightly mad effort to describe the history and geography of England and Wales – all of it”. He and Farley have a “common obsession” with the epic poem, McRae working on it as an academic researcher, and Farley rewriting it; when they met, they “got to thinking about creating a poly-vocal 21st-century version, capturing in poetry what the places of England and Wales mean to the people who inhabit them”.

So, deep in coastal Suffolk, Lisa Cherrett has pinned “rustling reed beds / tall stalks bend to the wind’s will / at the marshy edge”. On the Yorkshire coast, Julie Corbett writes of how “Red Campion edges the field / Vividly gashing the land / Whose medieval furrows / Seem like calm waves”. In Wales’s Langland Bay, Jim Young’s Sea Swimmer in Winter glories in the water: “Beyond the breeze, / under the winter sun, / the sea is calling me, / calling me, / calling me.” And in south London, John Davison mourns: “They’ve opened a Costa in Deptford, / I can’t quite believe that it’s true / They must have researched the wrong postcodes and they’re not serving chicken or stew.” Despite the map originally being planned for just England and Wales, there are also poems for locations in Scotland too – like James Fountain’s poem Glasgow Central – The Last Stop: “The train surges forward, and I grip / your memory, moving away from / home territory toward yours, / where I met you years ago, / stalking me like prey.”

McRae says the quality of submissions has been very high. “We’ve had one writer producing a series of 24 poems about Southend, another leading outdoor workshops in Rye, and others writing in response to the events we’ve been staging with partners in different parts of the country, and some school groups writing about the history and reputations of their localities. A bunch of poems pinned by a school in Long Eaton were quite moving – children in their early teens thinking through the history of their town and challenging preconceptions that other people might bring to it.”

Poly-Olbion was originally published with engraver William Hole’s highly decorative county maps. In this modern version, a two-layered map – where detailed Ordnance Survey data is overlaid with a map of England and Wales modelled on Hole’s 17th-century version – allows poets to pin their poems to the exact location they describe. Members of the public will be joined by the project’s official poets in residence – who include major names from Gillian Clarke to Sean O’Brien, Daljit Nagra to Jen Hadfield – holding workshops in heritage sites around the country.

“We wanted to answer the question of what our research, in the arts and humanities, can do for people who don’t feel inclined to read Poly-Olbion. It’s an effort to connect with writers of all ages and backgrounds, drawing them on to the same platform to address the same questions about place, heritage and identity,” says McRae. “We hope the map will inspire people to write, whatever their age or experience, and fill the map with thousands of new poems about places that mean something to them ... We want to celebrate the diversity, history and character of the places around us.”

• The Places of Poetry website will be live until 4 October, when it will close to new entries but remain open for readers.