BP's woes over the Deepwater Horizon oil disaster increased today when the company's latest attempt to contain the spill foundered as a result of a saw getting stuck in the pipe from which the oil was gushing.

Remote-controlled equipment on the sea bed, a mile beneath the surface in the Gulf of Mexico, positioned a diamond-edged saw against the bottom of the damaged pipe from which up to 19,000 barrels of oil are spewing daily.

Engineers were hoping to make a clean cut across the pipe to allow a custom-built cap to be put on top, to siphon the oil to tankers on the surface. But after the saw jammed, a second device had to be taken down from a nearby ship, further delaying efforts to contain the spill, which is now in its fifth week.

Admiral Thad Allen, leader of the federal response to the disaster, said: "Anybody that has ever used a saw knows every once in a while it will bind up. That's kind of what's happening there." But later a source close to the operation said the operation to free the saw had been a success and the operation was continuing.

BP's chief executive, Tony Hayward, said today that the oil industry might have to change the way it operated in extracting deep-water oil. He told the Financial Times: "We have been driving safe, reliable, operations through the company within the existing industry paradigm. What this causes us to question is whether that paradigm is right for the future."

He conceded that BP had not been fully prepared to deal with the deep-water blow-out on 20 April. "What is undoubtedly true is that we did not have the tools you would want in your tool kit."

BP's survival as an independent company is now being openly discussed in the City. Its share price continued to tumble today following the failed well-capping. Analysts are wondering whether merger talks – as happened between BP and its arch rival Shell in 2007 – might arise again as BP's ability to pay dividends is questioned, and its public credibility in America, which provides 40% of its income, plummets.

BP's share price fell 3% in early trading on top of the double-digit falls seen on Tuesday, and it has now lost a third of its value (equating to £44bn) since the Deepwater Horizon explosion. "If BP's share price continues to fall, it could become a takeover target," said David Buik, a financial commentator at the brokerage BGC Partners in London. "There are so many imponderables over whether its liabilities would be capped or not." He said Hayward's position seemed vulnerable.

Hayward's handling of the crisis has come under scrutiny following a series of gaffes. On Wednesday, he was forced to apologise for saying: "I want my life back". He said the remark had been "hurtful and thoughtless" especially to the families of the 11 men who died in the well explosion.

To add to the oil company's problems, the wind has shifted and is now blowing the huge oil slick towards Florida. Authorities there have been laying booms along the threatened shoreline, anticipating the arrival of oil by the end of the week. Oil slicks have already polluted barrier islands off Alabama and Mississippi, and more than 100 miles of coastline in Louisiana.

Speculation about BP's future intensified after the US attorney general, Eric Holder, announced a criminal investigation of the disaster, though he did not specify BP by name.

Analysts agreed that doubts about BP's prospects were inevitable while the crisis continued. Kim Fustier, oil analyst with Credit Suisse, in London, said the risk of a dividend cut was clearly rising since potential spill liabilities could reach $37bn. But Fustier was not willing to comment on whether BP was a possible takeover target. Shell, which announced a $4.7bn cash purchase of the US shale gas producer East Resources last week, said it never responded to that kind of speculation.

The previous chief executive of BP, Lord Browne of Madingley, revealed in a recent autobiography entitled Beyond Business that he took BP to the brink of a merger with Shell six years ago only to be thwarted at the last minute by opposition from a handful of his own board members. "We missed the boat. We estimated that a merger could create synergies of around $9bn a year in three to five years' time."

But there were also reports that Hayward had held similar discussions in 2007 when BP's share price had been weakened by the Texas City refinery fire, in which 15 workers died. The plunging value of BP is a blow to British pension funds as it is estimated to provide £1 in every £7 paid in dividends by FTSE-100 companies. BP is also a big provider of revenue to the exchequer. It said last night that it paid $6.3bn in global corporate income tax, of which $1.1bn (£690m) was in the UK. BP expects to pay about $4bn in 2009 in production taxes globally, of which £130m would be in Britain.

Duncan Exley, of lobby organisation FairPensions, cautioned investors: "Social and corporate governance issues have a history of precipitating crises which damage our economy and our investments."