The fund BP set up to deal with compensation claims after 2010's Gulf of Mexico oil spill is starting to wind down after paying out around $4 billion of the $20 billion set aside by the oil firm, the Sunday Telegraph reported.

The newspaper said Ken Feinberg, the lawyer in charge of the fund, had processed more than 80 percent of the claims submitted by those who suffered economically following the Deepwater Horizon accident, and so far used just over $4 billion.

I don't envision a flood of new claims, the paper quotes Feinberg as saying. Eight regional offices had been closed, it added.

The oil major established the fund last June for victims such as fishermen and property owners.

In an interview with Reuters in April, Feinberg said the fund was working as intended, though some local officials and advocacy groups alleged that the money was being distributed slowly and unfairly.

BP has estimated that the total cost of capping the well, cleaning up the damage from America's largest-ever offshore oil spill and compensating those affected will be more than $41 billion, including fines.

(Reporting by Rosalba O'Brien; Editing by Jon Loades-Carter)

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