The call for changes came as the losing side was sucked into a bitter blame game within hours of the bid's collapse, with Enterprise controlling just 33 per cent of Lasmo's equity.
As about 500 Enterprise staff gathered for a subdued 10th anniversary party at London's St James's Square on Friday, much of the flak was being directed at SG Warburg, the company's main financial adviser, for the bid's failure. Enterprise's other advisers were James Capel, Fleming and Lehman Brothers.
While Rudolph Agnew, Lasmo's chairman, was celebrating with champagne, the view was emerging in the City that Mr Hearne's dominant style was also to blame and that he would be forced to split the roles before the summer was out.
Some of Enterprise's advisers say that Warburg played the most crucial role in devising the ill-fated all-paper offer, comprising a mix of warrants and a new class of Enterprise paper.
The merchant bank is also understood to have been instrumental in arguing for the controversial purchase of nearly 10 per cent of Lasmo last week for an outlay of pounds 170m.
Most of the shares were bought at 169p, substantially above Lasmo's market price, from the fund manager PDFM - a move that subsequently antagonised other institutional shareholders, who felt they had been left out of the deal.
With Lasmo's shares closing at 137p last week, Enterprise is already nursing a pounds 32m paper loss on its shopping spree.
'At the end of the day the bid failed because one adviser dominated the entire campaign. The structure of the offer was entirely Warburg's creation, and they were also behind the presentation of Enterprise's arguments for the bid,' a member of the losing side said.
It has also emerged that some of Enterprise's directors were concerned about the conduct of the bid by Mr Hearne and fellow director Julian West. The duo failed to convince shareholders of the commercial logic for the bid, and the importance they attached to boosting Enterprise's size was a particular turn-off for City investors.
Launching the bid to a sceptical market two months ago, Mr Hearne declared: 'You need size and scale to make meaningful and lasting progress. This is a big boys' game, and Lasmo will give us the next step we need.'
But the bid's collapse is likely to undermine his dominance of the group's board - increasingly evident since John Walmsley resigned as finance director last year after boardroom differences.
Insiders say that the company could accept the need for a chief executive from outside in the near future.
David Stedman, oil analyst at Daiwa Research, said: 'There is bound to be some pressure from shareholders to split the roles. There must be some question marks about Enterprise's future direction. The traditional premium that the company's share price has enjoyed could be eroded.'
With Lasmo beyond reach, speculation is mounting that Enterprise may want to acquire Monument Oil & Gas, the North Sea explorer, in an agreed bid later this year.
Mr Hearne and Tony Craven Walker, his counterpart at Monument, held informal discussions late last year but could not agree on a price.
With Monument valued at about pounds 500m, it would be a much smaller catch for Enterprise but would be risky move.
Meanwhile, Lasmo wants Enterprise to place its 10 per cent stake.
The bid has cost Lasmo about pounds 25m to defend while Enterprise faces a pounds 7m bill. Had it succeeded, the company would have faced a bill of about pounds 15m, pounds 10m of which would have gone to Warburg.
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