Campaigners said pushing ahead with the project would “do nothing to tackle high bills or shore up energy security”.
Work on the proposed development off the west coast of Shetland was paused in December after Shell decided to withdraw from the scheme, concluding the economic case for investment was “not strong enough”.
However, the price of oil has since risen to more than 100 dollars (£76) a barrel, with fears over the future of Russian oil sending prices soaring.
There have also been calls to boost energy security by increasing North Sea oil and gas drilling.
Sources told the BBC that although Shell’s official position remains the same, it did acknowledge the “economic, political and regulatory environment had changed enormously” in the three months since Shell announced it was pulling out of the project.
Industry body Offshore Energies UK – formerly Oil and Gas UK – previously said blocking long-planned energy projects such as Cambo would risk leaving the UK at the mercy of global energy shortages.
Shell’s decision to pull out was announced just weeks after the UN Cop26 climate summit in Glasgow, where countries pledged to try to limit global warming to 1.5C to avoid the worst impacts of an overheating planet.
The International Energy Agency has said that no new oil and gas exploration projects should go ahead if the world is to meet the 1.5C goal.
And the advisory Climate Change Committee has said high prices are driven by global markets and increasing UK fossil fuel extraction would have virtually no impact on bills, urging efforts to cut oil and gas demand instead.
Philip Evans, oil and gas transition campaigner for Greenpeace UK, said the Cambo project would “do nothing to tackle high bills or shore up energy security”.
He said: “Shell wasn’t interested in pursuing this project when it was a bad look for them, but now they stand to gain billions in the midst of wartime price hikes, they’re interested again.
“Meanwhile our bills soar, and offshore workers are trapped in a volatile industry.
“The UK and North Sea communities deserve better.
“With the spring statement and a new energy strategy coming up, the Government must throw its weight behind British renewables, a proper home insulation scheme and heat pump rollout, or our energy policy will be disrupted by the whims of fossil fuel giants for decades.”
Scottish Greens energy and climate spokesman Mark Ruskell said: “Opening the Cambo oil field makes even less sense today than it did last year.
"Any u-turn from Shell would be based purely on maximising its already eye-watering profits, it certainly wouldn’t help with soaring energy bills or our energy security.
"The fact is most crude oil extracted from this site would be exported so it would have little impact on energy security and be massive blow to the transition away from fossil fuels.
"And if we are going to tackle Putin’s power and the impact rising energy bills are having on the cost of living, we need to reduce our reliance on oil and gas and invest in renewable energy.
"The UK Government must stop using the war in Ukraine as an excuse to abandon climate commitments.
"Next week’s energy supply strategy has to recognise the UN’s call that the transition to clean energy is a global security imperative, as well as being the only way we meet climate targets and secure a future.”
But Liam Kerr, the Scottish Tory spokesman for energy, net zero and transport, said Ms Sturgeon's decision to “abandon North Sea oil and gas undoubtedly shook confidence in the sector”.
He said: "This SNP-Green coalition would turn off the taps in the North Sea tomorrow if they could.
"The Scottish Conservatives repeatedly warned them, and Labour, about the ramifications for domestic energy security — and Putin’s appalling invasion of Ukraine has brought into even sharper focus the importance of not relying on foreign oil and gas imports.
"Their dogmatic refusal to change course looks more reckless by the day, so Nicola Sturgeon must admit she’s got this wrong and give her backing to Scottish oil and gas production — and the tens of thousands of skilled jobs it supports.”