If production is approved, oil and gas will be pumped up through a large ship 80 miles north west of Shetland
Labour MPs have called on the government to reject the Rosebank oil field, saying it is "incompatible" with the UK's climate commitments.
There is a growing expectation among senior Labour figures that drilling in the oil field off the north-west coast of Shetland will be given the go-ahead.
Prime Minister Andy Burnham said on Wednesday that a decision would be "taken in due course" while Energy Secretary Miatta Fahnbulleh stressed that affordability of energy bills was her "overriding objective".
But in a sign of the division within the party, about a dozen Labour MPs expressed concerns about approving it during a Westminster Hall debate in Parliament.
Separately, it is understood some Labour backbenchers have organised a letter opposing Rosebank - intended for Burnham, but not yet sent - which more than 60 out of about 400 Labour MPs have indicated they support.
One signatory told the BBC that approving Rosebank "would not create new jobs, would bring minimal money into the Treasury and be bad for the climate".
"The government's central aim is to tackle the cost of living crisis, and drilling for more oil at Rosebank isn't the answer," the MP said.
Wednesday's Westminster Hall - a type of parliamentary debate where backbench MPs raise topical issues but do not vote - was organised by Green MP Carla Denyer.
Labour MP for Sheffield Central Abtisam Mohamed told the debate: "Rosebank fails on every test.
"It will not benefit taxpayers who will shoulder the vast majority of the development costs, it will not strengthen our energy security because most of the oil will be sold on international markets, and it will not reduce energy bills for our constituents, who will remain exposed to volatile fossil fuel prices."
Richard Burgon, a former frontbencher on the left of the party, said: "Rosebank is not compatible with our climate targets - it's dangerous to pretend otherwise."
The UK is committed to reaching net zero by 2050 and wants to limit global warming to no more than 1.5C above the pre-industrial period.
The UK government has always insisted that Rosebank is a quasi-judicial decision, formally resting with Fahnbulleh. She green-lit production in the Jackdaw gas field in the North Sea last month, but Rosebank hangs in the balance.
Energy Secretary Miatta Fahnbulleh will formally announce the Rosebank decision, expected in the coming weeks
Labour's manifesto upon entering power in 2024 pledged not to "issue new licences to explore new fields".
Licences for both Jackdaw and Rosebank were granted by the then Conservative UK government in 2022 and 2023 respectively.
But the Court of Session in Edinburgh ruled last year that the government had made the approvals unlawfully, leaving the current Labour government to make a fresh decision on whether to give the go-ahead.
Conservative leader Kemi Badenoch sought to tease at Labour divisions on the issue during Prime Minister's Questions on Wednesday.
Demand for fossil fuels
During the debate, Labour MP Anna Gelderd said: "We live in an unprecedented era where our energy security is more vital than ever, in which jobs and wealth must be protected and economic opportunities seized - on both of these points, Rosebank fails."
Labour MP Julia Buckley said she had received opposition to Rosebank from her constituents in "regularly flooded Shrewsbury" and said fossil fuels "belong in the past, not the future".
She urged Fahnbulleh to "reject the oil licence in favour of renewables", adding: "Please don't add further to our climate emergency."
Other Labour MPs expressed their support, including recently departed veterans minister Al Carns, who warned that Britain would continue to need fossil fuels for decades and importing more would be a mistake.
"Refusing to produce it here does nothing on its own to eliminate that demand - it simply increases our reliance on imports which can carry their own environmental cost," he added.
Those representing communities with ties to the oil and gas industry, including Jonathan Brash, the Labour MP for Hartlepool, stressed the benefits of approving Rosebank for British jobs.
Energy minister Michael Shanks told the debate the government would take a "pragmatic approach" to a clean energy transition, stressing it was "not a turn off the taps government, but nor can we justifiably be a drill every last drop government either".
"This government will not make decisions for this country which are not compatible with our climate obligations," he added.
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