BP is self-insured and will have to foot the majority of the £1bn worth of liability claims arising from last week's Texas refinery explosion.
However it is understood Willis is involved in some of the claims.
Sources at Lloyd's said BP was largely self-insured, and would therefore have to meet any casualty and property losses from its own reserves.
The explosion killed 15 workers and injured 100.
BP spokesman Roddy Kennedy said: "We do not insure except in areas where we have statutory coverage. Insurance is too expensive for the oil industry."
Damage to the refinery, litigation costs, workers' compensation and medical fees will cost the oil giant up to £1bn according to experts.
BP chief executive Lord Browne described the blast at the 1,200 acre refinery plant in Texas City, as "the worst tragedy that I have known during my time with BP."
Willis was unavailable for comment.
Hosted by comedian and actor Tom Allen, 34 Gold, 23 Silver and 22 Bronze awards were handed out across an amazing 34 categories recognising brilliance and innovation right across the breadth of UK general insurance.
