Royal Bank of Scotland saw its stock market value rise by as much as £900 million after Chancellor George Osborne announced plans to begin selling off the taxpayer's stake in it.
Shares climbed by around 2% though some City analysts questioned the timing of the announcement and one expert suggested it was unlikely that taxpayers would ever get all their money back after ploughing nearly £46 billion into saving RBS.
The Government owns 79% of the bank after rescuing it from collapse at the height of the financial crisis seven years ago.
Mr Osborne admitted in his Mansion House speech to the City last night that it stands to make a loss of about £7 billion if the entire stake is sold off in one go.
But he cited an analysis by Rothschild finding there would be an overall profit of £14 billion if all the Government's remaining shares in all the bailed-out banks were sold.
Labour claimed the Chancellor's logic was "dubious" and said taxpayers would be suspicious of any "rush to sell".
There were also question marks over the analysis in a report in The Times which suggested the £14 billion profit would be wiped out by the £18 billion cost borne by the Treasury to pay interest on the money it borrowed to finance the bail-outs.
Michael Hewson, chief market analyst at CMC Markets, said on RBS: "The fact remains it is unlikely that the UK taxpayer will ever get all of its money back and if anyone thinks otherwise, they are inhabiting a different universe to the rest of us.
"It makes more sense to get the bank back on its feet, off the Government's books and to go back to trading as a going concern free of state support, contributing to the Exchequer that way over the next 20 to 30 years."
Investec banking expert Ian Gordon said: "The timing of last night's announcement was arguably somewhat premature, dictated more by politics rather than, necessarily, an exercise in optimising market timing."
Graham Spooner, investment research analyst at The Share Centre, said: "It appears that the Government feels the shares will be better off in the hands of investors.
"However, the sale is expected to be a difficult one, as the bank is still on the road to recovery and has reported seven years of losses since the bail-out.
"We remain cautious on RBS and believe there are better opportunities for followers of the banking sector."
Mr Osborne told a City audience that beginning to sell the RBS stake in the coming months was "the right thing to do for British businesses and British taxpayers".
"Yes, we may get a lower price than Labour paid for it. But the longer we wait, the higher the price the whole economy will pay.
"And when you take the banks in total, we're making sure taxpayers get back billions more than they were forced to put in.
"From bailing out the banks to bringing them back from the brink, now is the time for RBS to rebuild itself as a commercial bank no longer reliant on the state, but serving the working people of Britain."
In a letter to the Chancellor, Bank of England governor Mark Carney said public ownership of RBS had "largely served its purpose" and a "phased return" to private ownership would promote financial stability.
"Continued public ownership without a foreseeable end point runs risks, including limiting RBS's future strategic options, and continuing the perception that taxpayers bear responsibility for RBS losses," he said.
"In these regards, there could be considerable net costs to taxpayers of further delaying the start of a sale."
Shadow chancellorChris Leslie said: "Taxpayers who bailed out RBS want their money back in full and will rightly be suspicious of any rush to sell.
"When RBS is still restructuring the business, and awaiting a US settlement for the mis-selling of sub-prime mortgages, a premature sale poses a risk for taxpayers.
"It is highly dubious for the Chancellor to claim that significant losses on RBS are somehow acceptable because a gain can be made selling Lloyds or other completely separate assets.
"The Chancellor said two years ago that he would only countenance a sale of RBS when 'the bank is fully able to support our economy and when we get good value'. Neither of these tests have yet been passed."