A group of Nigerians, led by some aggrieved indigenes of Ogoniland, on Friday took their campaign against Shell Petroleum Development Company (SPDC) to the London High Court, seeking tens of millions of dollars in compensation for two oil spills in 2008, which they claim destroyed their source of livelihoods.

SPDC, operator of the joint venture between Nigerian National Petroleum Corporation (NNPC) on behalf of Shell, Total and Agip, has admitted responsibility for the two spills that affected the Bodo fishing communities in the Niger Delta.

But Shell and the London lawyers representing the claimants disagree about how much oil was spilt and how much compensation they should get. Talks to resolve it broke down last week.

“They made an offer and the community quite rightly said this is ridiculously low,” said Martyn Day, of the London law firm, Leigh Day & Co, who is leading legal proceedings.

Though Mr. Day said he hoped negotiations resume with Shell at some point, he declined to say how much Shell had offered.

He said his clients would be claiming “many millions of dollars” through the High Court, but there was no precise figure, because there were 11,000 claimants so far, but more might join the action later.

Shell says 4,000 barrels of oil in total were spilt in Bodo in 2008 as a result of operational failures and a clean-up was completed in 2009. It says that since then, more oil has been spilt due to sabotage and oil theft, known as “bunkering”.

“Our clean-up teams were able to deal with the initial operational spills, but subsequently they have been prevented by local communities from reaching sites that were reimpacted by this illegal activity,” said Mutiu Sunmonu, SPDC managing director, in a letter to the Financial Times on Wednesday.

“This could be because those communities hold a misguided belief that more spilt oil, irrespective of the cause, equals more compensation.”

Mr. Day disputed the figures, saying experts had put the volume spilt because of Shell’s two operational failures at 600,000 barrels, and that any bunkering that took place in the area would account for no more than 1 percent of that.

In a report in November 2011, human rights group, Amnesty International blamed Shell for spilling 280,000 barrels in Bodo and called on it to pay $1 billion to clean up the Niger Delta.

If the figures given by AI or by Mr. Day are close to the truth, that would make the Bodo spill one of the biggest in history. By comparison, the volume spilt in Alaska in the Exxon Valdez disaster was estimated at 257,000 barrels.

The discrepancies between the different estimates of the Bodo spills illustrate how hard it is to get an accurate picture of what goes on in the remote creeks of the Delta.

In a region where millions of people scrape a living from subsistence fishing or farming and live in mud-huts with no electricity, the presence for decades of a multi-billion-dollar oil industry with its high-tech equipment and luxurious compounds for expatriate workers has led to deep resentment.

Pipeline sabotage by militants campaigning for a greater share of oil revenues, or by local criminals looking to benefit from clean-up contracts, are common there.

Mr. Sunmonu gave a flavour of this on Friday when he told BBC Radio 4 that the company wanted to help, but there was “lots of intra-communal strife making it difficult for anyone to have meaningful negotiations”. He said lots of people who claimed to have been affected by the Bodo spills were lying.

The Bodo case is particularly troublesome for Shell because the area is in Ogoniland, a part of the Delta that was the scene of one of the company’s worst public relations disasters.

In 1995, nine Ogoni activists including the environmentalist Ken Saro-Wiwa, who had been campaigning against Shell’s activities in his homeland, were tried on trumped-up charges and hanged by the then military dictatorship of Sani Abacha.

Saro-Wiwa has become a martyr to many environmental activists around the world. Although Shell was not directly responsible for his death, it was widely blamed for cooperating with Abacha’s brutal and corrupt regime.