The Government’s carefully orchestrated auction of Northern Rock was unravelling last night after one bidder walked away and another appeared to be falling out of the race.

It is understood that JC Flowers, the American private equity firm, has told the Treasury that it would no longer compete for the stricken mortgage bank because it could not structure a deal that would keep both the Government and shareholders happy.

A bid from Olivant, the investment group run by Luqman Arnold, was also hanging in the balance after it emerged that the firm was refusing to sweeten its takeover proposal. One source said: “It’s absolutely painful. There are so many people involved and so many different agendas.”

Advisers to Olivant were last night fine-tuning its offer, but had ruled out making any major concessions on the terms.

The Northern Rock camp was understood to be lukewarm on the Olivant deal, due to be unveiled this morning, in its present form.

One source close to the Rock said that if the cash portion of the offer was not raised, Mr Arnold’s group would have little chance of competing. “I think unless Olivant has a similar amount of equity to Virgin, I can’t see how it’s going to work,” the source said. “He needs to come up with a lot more equity if he’s going to get the banks to lend.”

Northern Rock, which nearly collapsed earlier this year in the wake of the US sub-prime crisis, has named Sir Richard Branson’s Virgin Group as its preferred buyer. However, aided by pressure from the Treasury in recent days, rival bidders including JC Flowers and Cerberus have received more serious consideration from the bank’s management and advisers.

JC Flowers had submitted a second offer for the Rock in which it offered immediately to repay £15billion of Bank of England loans and inject £1billion of equity upfront. However, one source last night said that the proposal did little to satisfy the demands of shareholders who feared they their holdings would be significantly diluted as part of the proposal.

Olivant, set up and run by Mr Arnold, the former Abbey National boss, has proposed taking an equity stake of about 15 per cent and making Mr Arnold interim chief executive, in place of outgoing chief executive Adam Applegarth, the outgoing chief executive. The proposal has won support from is backed by leading Rock shareholders who, under the plan, would be left with 85 per cent of the bank and thereby would stand to benefit most from a recovery.

Olivant is also planning a rights issue, thought to be for about £500 million.

It is understood that JC Flowers will keep its bid on the table but no longer plans to compete in the auction. This will leave Virgin and Cerberus, the American investment firm, as the two main contenders.

The stricken lender is known to have received at least four serious bids, although it is understood that none of the suitors has yet secured the backing of any of the commercial banks to provide the billions of pounds worth of loans needed to prop up Northern Rock and pay back the Bank of England.

One source said last night: “They’ve got the funding in theory, but theory is a long way from reality.”

Olivant’s bid, boosted in the past few days by the naming of Lehman Brothers as broker, comes as Northern Rock yesterday admitted that it had so far borrowed £25 billion from the Bank of England. The admission by the embattled Tyneside bank is its first acknowledgement of the size of its borrowings.

The Rock denied it was behind a further £5 billion of loans by the Bank disclosed this week in its accounts as “other assets” earlier this week. It is understood that the Bank has also carried out transactions with the UK Government, foreign central banks and international financial institutions. It confirmed the £25 billion figure, but declined to comment further.

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