Cornish MPs have called on Sir Keir Starmer to grant the region devolution powers akin to Wales in the King's Speech.
Ben Maguire and Andrew George, part of the cohort of new Liberal Democrat MPs, said the area's "unique" historical and cultural identity warrants a "unique" model of governance.
Labour has pledged to kickstart a new "devolution revolution" to boost economic growth, with a new "take back control" bill expected to be a key feature of the King's Speech on Wednesday.
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In a letter to the prime minister, the two MPs said they welcomed that commitment and that it was in line with Cornwall's "long-standing ambition to secure substantially greater decision-making powers and a Cornish assembly".
Mr Maguire, the MP for North Cornwall, told Sky News this would be a devolved law-making assembly along the lines of the Senedd (Welsh parliament).
He said Cornwall's "cultural distinctiveness and heritage", as a duchy which once had its own king and language, meant it was deserving of a special arrangement.
"A lot of people in Cornwall do see themselves on a level of the other Celtic nations and therefore deserving special status," he said.
"The Cornish language is a very unique thing which has protected status. Cornish people have a protected status.
"Angela Rayner has asked all of us if you want local devolution then seize it and that's what we are doing."
Ms Rayner, the deputy prime minister and communities secretary, wrote to local authorities in "devolution deserts" on Tuesday telling them the door is open if they want extra powers.
It is not clear what the new devolution deals could look like - with more details expected to be laid out during the state opening of parliament tomorrow, when Labour will set out its legislative agenda for the year.
Only around half of the people in England currently benefit from a devolution deal.
Labour said that in areas with metro mayors, like Greater Manchester, there has been greater economic growth thanks to local powers to attract new investment.
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However last year, Cornwall's Conservative-led council abandoned plans for that model following local opposition, with a "level 2" deal agreed that would grant greater powers over skills and green energy but come without a £360m mayoral investment fund.
Mr Maguire, who gained his seat from the Tories after they were all but wiped out in the South West at the election, said he did not support the mayor model as it is "putting all the power into one person".
He said an assembly model would allow for fuller scrutiny because it means "direct representation from each part of Cornwall".
It would also allow the region to retain 100% of its business rates - with about 50% currently going to Westminster - money which could be used to create affordable housing as the region grapples with a property crisis driven largely by second homes and holiday lets.
The issue has started to have a knock-on effect on schools, with one primary school warning earlier this year that it could be forced to close as families are being priced out of the village.
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Tap hereMr Maguire, who swore into parliament in Cornish last week, said: "It [the current devolution arrangement] doesn't go far enough, it's window dressing, it doesn't give the powers Cornwall needs in terms of addressing the housing injustices.
"Another big issue is discrepancy in per pupil education funding. Things like that that could be addressed if we had a full devolution deal rather than getting the scraps from Westminster.
"This is a historic opportunity to finally recognise Cornwall's cultural distinctiveness and heritage and finally address the injustices and inequalities of being so far from Westminster."
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