BP is desperately hoping its first relief well will be finished by the time it reports second quarter results on 27 July and could have good news as early as the 20th, though much will depend on a mild hurricane season.The company, currently busy buttering up sovereign wealth funds in the Middle East, has always stated the fix would be in place by the middle of August.But British prime minister David Cameron is dropping in at the White House on 20 July and would like to be the bearer of good news."In a perfect world with no interruptions, it is possible to be ready to stop the well between July 20 and July 27," Bob Dudley, head of BP's Gulf Coast restoration unit, has told Wall Street Journal.The plan could trip up though as Dudley admits this "perfect case" is threatened by the hurricane season and is "unlikely".BP is also working on a Plan B that involves connecting the well to pipelines in two nearby underwater gas and oil fields.It has been under intense pressure to get things sorted in the Gulf as the environmental disaster, already the biggest in American history worsens.The broker Deepwater Horizon well has been leaking oil in the sea at a rate of anything up to 100,000 barrels a day and has so far cost BP over $3bn in clean-up costs alone.Chief executive Tony Hayward met with Abu Dhabi crown prince Mohammed bin Zayed Al Nahyan yesterday and is apparantly comfortable with him taking a stake of up to 10% in the oil giant. BP's share price has halved since the explosion on 20 April killing 11 workers, and traded below 300p two weeks ago for the first time in 14 years. The governments of Kuwait, China, Singapore and Libya are also thought to be interested in injecting funds.