Shares in BP fell nearly 5% this morning after the company warned that the cost of tackling the disastrous oil spill in the Gulf of Mexico now exceeds $6m (£4m) per day, and will keep rising as it intensifies its efforts to deal with the accident.

The British energy giant told the stock market that it has begun drilling a 'relief well' to try to isolate the original well which is still spewing 5,000 barrels of oil into the sea each day. This involves digging 13,000 feet below the seabed, and BP estimated today that this could take around three months.

The company also said in a statement that, contrary to some reports, it has not managed to slow the flow of oil from the MC252 well.

BP shares dropped to a low of 546p when trading in London began as City investors took their first opportunity to offload BP shares following the long weekend. This knocked more than £5bn off last Friday's market capitalisation taking it to around £102.5bn. At the start of last week, the company was valued at £122bn.

With chief executive Tony Hayward due to meet US politicians and regulators in Washington later today, the company is attempting new ways to deal with the disaster. The latest idea is to inject dispersants directly into the oil flow close to the main leak:

The technique is intended to efficiently mix the oil and dispersant, breaking up and dispersing accumulations of oil and allowing it to degrade naturally and reduce surface impact. The suggestion for this innovative technique came from the companies across the oil industry that BP approached last week for further ideas and expertise to help BP control the well and tackle the spill.

BP also hopes to erect a steel canopy over the leak point, allowing it to corall the oil and then pump it to the surface. Depending on the weather, it may try to install a "coffer dam" in the middle of next week.

It also continues to operate eight submersible robots in an effort to activate the blowout protector, which is meant to seal a well and stop oil leaking out.

BP, which hired the Deepwater Horizon rig that caught fire and sank two weeks ago, said it continues to cover the cost of these various efforts, and warned shareholders that it does not know what the final bill will be:

Whilst difficult to accurately estimate, the cost to the MC252 owners of the efforts to contain the spill and secure the well is currently estimated to be more than $6m per day. This figure is rising as activity increases. It is too early to quantify other potential costs and liabilities associated with the incident.

Until BP can stop the oil leak, it will be impossible to estimate quite how badly this drama will play out. On a financial level, independent estimates have put the final bill at anywhere between $3bn and $12bn (£2bn- £7.8bn).

In other City news this morning.... Ryanair has urged passengers not to panic as another cloud of volcanic ash hits Ireland. Irish regulators have closed airspace, but say they "hope to have positive news" later today. Ryanair itself has declaed that the disruption will not be as bad as last time.

And in banking, Standard Chartered's focus on Asia continues to pay off with a record-breaking performance in the first three months of 2010. It announced this morning that its wholesale banking arm (which includes investment banking) saw a 20% jump in client income as customers continue to seek financing, and foreign exchange deals.

Encouragingly, there were no significant new bad debts in its corporate loan book.