Shareholders lost their High Court case in February
Former Northern Rock shareholders have lost their appeal in the latest stage of their challenge to the government's compensation plan.
The shareholders had appealed against a High Court decision to refuse a judicial review of the fairness of the government's scheme to compensate them.
They argued the government had deliberately undervalued the bank in the run up to its nationalisation.
But they said that they would now try to take the case to the House of Lords.
"We embarked upon this legal challenge in the full expectation that it would be a lengthy process. We are determined to see it through to its conclusion," said Jon Wood, of SRM - which was involved in bringing the appeal.
Northern Rock came close to collapse at the start of the credit crisis in 2007 after savers staged a run on the bank after it had sought financial aid from the government.
Subsequently it had to be bailed out by the government, which then went on to nationalise the bank in February 2008.
At the time of nationalisation the government said that any subsequent valuation for compensation purposes should be based on the assumption that Northern Rock had not been a going concern.
The appeal was brought by hedge funds and other Northern Rock shareholders.
They argued in the original High Court case that the government's assessment of the bank's true worth was false and almost guaranteed that they would end up with nothing.
Government barristers pointed out that the lender had been lent or guaranteed £54bn of taxpayers money to keep the bank going, and that without this support the bank would have gone bust, leaving the shares totally worthless.
The High Court judges ruled that shareholders had taken a commercial risk with their investment.