The former Smiths guitarist and co-songwriter - along with Morrissey - is a huge fan of the 'Cake' star and teamed up with her for the moving track about the plight of homelessness.
The song is based on the real-life experiences of former Big Issue magazine seller Joe Gallagher, and how he survived on the streets of Edinburgh.
For the track, Marr's music is accompanied with Peake reading out poetry penned by Gallagher.
On how the collaboration came about, Marr said: ''I wanted to do something different and I thought of asking Maxine to collaborate having been a fan of her work.
''We started a creative process that clicked and culminated in 'The Priest', a song and short film inspired by a facet of modern life as we see it and feel it.''
The song, which is out now, has been released alongside a short film, which was shot in Marr's home city of Manchester and features Molly Windsor, Peake's 'Three Girls' co-star, in the lead role.
The track will be followed up by his third solo album, which is inspired by the effects on the world of Donald Trump's ascent to become President of the United States and Brexit in the UK.
The 54-year-old rocker is putting the finishing touches to the follow-up to 2014's 'Playland', which is due to be released in spring 2018.
Marr admitted the turbulent political climate has found its way into his songs because the influence of British residents voting to leave the European Union and Trump's behaviour in the White House are hugely important to him.
He explained recently: ''I was trying to imagine an alternative society. Because of what had happened with Brexit and Trump and everything, I came into this record really determined to not let those f**kwits impede on my creative life
''But you're living in this world and you can't do anything about it. So much of the record is about dislocation. Whether it's being forced by the political system or because of personal demons. I was trying to imagine an alternative society.''
When Marr was a member of legendary rock band The Smiths, he and singer Morrissey were never afraid to tackle heavyweight social and political issues on albums such as 1985's 'Meat Is Murder' and 1986's 'The Queen Is Dead'.
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