Just weeks after Simon Armitage was named the UK’s next poet laureate, the contest for the country’s second most important role in poetry has begun. Voting has opened for Oxford University’s next professor of poetry, with two of the country’s best known practitioners, Alice Oswald and Andrew McMillan, both in the running.

Candidates for the four-year professorship, which involves giving a public lecture every term and is currently held by Armitage, must be nominated by at least 50 Oxford graduates. Oswald, the winner of the TS Eliot, Costa and Griffin prizes, was backed by the most supporters, with 167 throwing their weight behind her, including former poet laureate Andrew Motion, novelist Mark Haddon and biographer and academic Hermione Lee.

Yorkshire poet McMillan, whose debut Physical celebrated the male body and won him the Guardian first book award as well as a host of nominations for other major prizes, counts 84 supporters, while the British-Canadian poet Todd Swift has 60.

Each contender now has until 20 June to canvas Oxford graduates for their votes. Their opening sallies will be made on Thursday, as all three publish statements staking their claim on a role that was inaugurated in 1708, and has been held by Matthew Arnold, WH Auden and Robert Graves.

Oswald promises that if she were to be elected, she will look to stage “extreme poetry events” such as “all-night readings of long poems, poetry in the dark or in coloured light, even perhaps a Carnival of Translation, A Memory Palace, a Poem-Circus … or an exhibition of mobile poems”.

Her statement adds: “It’s exciting to be engaged in poetry at a time when its medium is changing almost as radically as it did in the eighth century BC. I see no reason why Instagram poems shouldn’t prove as rewarding as concrete poems or the visual poems of classical Chinese and I’d welcome the chance to invite young poets to engage in discussion about what poetry has been and is becoming.”

‘We’re witnessing a new generation of poets step forward’ ... Andrew McMillan. Photograph: Urszula Soltys

In his statement, McMillan also points to the “moment” poetry is having, with sales last year hitting an all-time high and readers under 34 accounting for two-thirds of sales.

“More than any time in the past two decades, we’re witnessing a new generation of poets step forward and claim space within the prize lists and the editorial boards and the inner rooms of our art form,” McMillan says. “The Oxford professor of poetry feels like a position uniquely suited to this current moment; both future-facing, towards the student body and yet with the weight and prestige of the lineage of predecessors standing behind it as well.”

At 30, McMillan concedes his relative youth, “though with half a decade on Keats, at his oldest”. He said he would “make a dynamic, insightful and fresh contribution”.

In the past, campaigning for the position has been controversial – in 2009, Ruth Padel resigned days after being elected, after it was claimed that she had told journalists about allegations of sexual harassment made against her rival Derek Walcott – and this year looks to be no different. Swift’s candidacy has prompted concern among some in the poetry community, a year after the Bookseller reported that his small press, Eyewear Publishing, had included a contract clause that forbade poets from contacting trade union the Society of Authors for assistance. Vida, the organisation for women in the literary arts, also published a lengthy complaint by the poet KC Trommer about Swift’s conduct on social media.

Planning to ‘ask questions of poetry, poets and poems’ … Todd Swift Photograph: PR

The Guardian understands that a group is currently drafting a letter to Oxford asking that Swift be removed from the contest, but Oxford said it had yet to receive any letter.

“Todd Swift is unsuitable for the role of Oxford professor of poetry, and the level of prestige it offers,” said poets Claire Trevien and Aaron Kent in a joint statement. “There are various accounts of his behaviour available with a simple Google/Twitter search, including the Bookseller’s report on his contracts interfering with authors’ civil rights, and the report on his behaviour through Vida. It is because of these actions that he should not be considered. The role would surely be better going to Alice Oswald so she could bring a female voice to a historically male-dominated role, or to Andrew McMillan who can bring a queer and working-class voice to the position.”

In his statement laying out why he should be considered for the role, Swift says he “would enjoy the chance to lecture on current trends in poetry, and as a gadfly of sorts continue to ask questions of poetry, poets and poems”.

The winning candidate will be announced on 21 June.