BP said in its earnings report that cumulative charges from the Deepwater Horizon accident in the Gulf of Mexico totaled $42.2 billion. The company in early May said it reached a deal with trustees in Alabama and Louisiana to provide $434 million to help with restoration related to the 2010 spill.
BP set aside billions of dollars for costs related to the spill but said it may have underestimated the total figures involved.
The first phase of a civil trial involving the 2010 oil spill in the Gulf of Mexico concluded April 17.
Sources in the company told the BBC that BP is worried that "alleged undeserved payments" may hurt its finances to the degree that it would be the target of a takeover bid.
The BBC, citing BP sources, said the rate at which cash is leaking from the company could turn into a serious financial crisis for BP.
The BBC adds that BP hopes Cameron will ask the U.S. government to intervene by raising the issue at the G8 summit next month.
Cameron said he was considered about allegations this week that BP was involved in a price-fixing scandal.