The Foinaven and Schiehallion fields, in the Atlantic, west of the Shetland Isles, are the great hope for the future of Britain's oil production industry with reserves worth billions of pounds. Exploiting the two fields would secure hundreds of jobs and bring in hundreds of millions of pounds in tax revenue.
But Greenpeace says the oil should be left undisturbed below the seabed to reduce the threat of man-made climate change. Whenever fossil fuels such as oil are burnt they produce carbon dioxide, which traps solar heat in the atmosphere, giving rise to the so-called "greenhouse effect".
It will be the first time Greenpeace has tried to stop an oilfield development on climate protection grounds.
``This should not come as a surprise,'' said Peter Melchett, the executive director of Greenpeace UK. ``At some point we are going to have to draw a line in the sand over this issue.''
Lord Melchett, a junior minister in the last Labour government, has written to the Prime Minister, John Major, to say that the production of oil on the "Atlantic frontier" west of Shetland was incompatible with Britain's declared aim of tackling the global warming threat. ``There is a very serious contradiction at the heart of your Government,'' he wrote.
``At international meetings you lead calls for action ... at home, in Britain's backyard, you encourage the exploitation of fossil fuel reserves.''
But Mr Major's four page reply said there was no case for banning fossil fuels, and that the area west of Shetland ``is being opened up for exploration in an environmentally sensitive manner.''
Greenpeace is not satisfied with this, and intends to keep putting pressure on the Government and the oil companies operating west of Shetland. BP has the largest interest, followed by Greenpeace's old Brent Spar adversary, Shell.
``We never rule out direct action. If we're going to survive as humans on this planet we have to protect the climate from drastic, destructive change,' said Lord Melchett. Greenpeace wants the big oil companies to invest in non-polluting, renewable energy sources like solar power instead of fossil fuels.
A spokesman for BP said there was no question of abandoning the Atlantic frontier.
``I guess we're going to have to disagree with Greenpeace. Everything we take for granted in our society - warmth, transport, plastics - comes from fossil fuels. But our solar-power subsidiary is one of our fastest growing divisions.''
The new fields would play an important part in sustaining oil production from the North Sea well into the next century, he added. Production is expected to go into a long, gradual decline after reaching its all-time peak this year.
The oil companies are investing some pounds 1.5bn in exploiting the Foinaven and Schiehallion fields, with most of the money spent in Britain. The reserves are put at over 400 million barrels, worth around pounds 4bn.
Bringing the oil in these areas to the surface is not easy. Oil companies must cope not only with the huge waves and high winds found in the North Sea, but also with much deeper water - well over 1,000 feet - and powerful, variable sea-bottom currents.
Extracting the oil requires a new, radically different production system. The wells are drilled from a floating rig, but the valves which control the flow of oil out of them are installed on the sea floor rather than on a platform at the surface. Because it is far too deep for divers the installation is carried out using remote-control, submersible equipment.
A huge tanker-like vessel, called a floating production system, is then anchored above the well-heads, and kept pointing into the wind and waves. The crude oil is carried up to it through hoses which are linked to a swivelling turret. The oil is stored on board and unloaded directly into visiting tankers. BP hopes to start production at the Foinaven field in the next few months.