A £3.21billion chunk of taxpayer-backed Lloyds Banking Group has been sold by the Government as it begins the process of returning the bank to private hands.

The stock was snapped up by institutional investors at a price of 75p per share, only a small discount to last night’s closing price on the FTSE 100 of 77.36p.

It means the taxpayer stake in Lloyds, rescued by the state at the height of the financial crisis after the disastrous acquisition of Halifax Bank of Scotland, has been reduced from 38.7% to 32.7%.

The sale price represents a £61 million profit on the 73.6p average price paid by the Government at the time. No further sale of the taxpayer stake will take place for a further 90 days.

The sale of 4.28 billion shares was announced by UK Financial Investments, which holds the taxpayer stakes in the rescued banks on behalf of the Government.

It will register as a paper profit of £586 million on the Government’s books because its stake in Lloyds is recorded in the public finances as 61p per share.

The reduced cost took into account the fact that the Treasury had already received £2.5 billion in relation to the asset protection scheme announced in 2009.

Chancellor George Osborne kicked off the share sale last night, five years after Lloyds was left needing a £20 billion bail-out.

The initial tranche was not made available to the public, though they are expected to participate at later stages of the bank’s re-privatisation.

The share sale comes ahead of the Conservatives’ annual party conference starting on September 29, and follows a run of upbeat economic news.

In recent months shares have also consistently traded above the 73.6p average price paid at the time of the bank’s £20.3 billion Government rescue.

The sale marks a milestone for Lloyds, which hailed its recovery earlier this summer after swinging out of the red with half-year profits of more than £2 billion.

On reporting the turnaround Lloyds boss Antonio Horta-Osorio said that it was up the Government to decide “when and how” to sell off its stake.

Last week the bank spun off a re-launched TSB with a spin-off of more than 600 branches which it was obliged to dispose of under European laws on state aid. The new bank is expected to be floated on the stock market next year.

Lloyds TSB shares opened 1.3p lower at 76.1p.

Mr Osborne hailed the sale as representing a half billion pound reduction in the national debt, though the Treasury made clear this figure based on paper profit would be subject to a decision by the Office for National Statistics.

He said the fact that “investors from around the world” had snapped up the stake showed the British economy was turning a corner.

The identity of the investors has not been disclosed though sources said the biggest single block was from the UK while the overall majority of shares have gone to UK or US buyers.

The sale was described as the second largest accelerated share sale of its kind, after a Barclays offering in 2009.

Mr Osborne said: “Five years ago the previous government forced British taxpayers to put a huge sum of money into bailing out the banks.

“That was a big ask of the British public. I have been determined ever since I became Chancellor to get that money back for taxpayers.

“I can confirm this morning that we have sold 6% of Lloyds Bank at 75p a share. That is a profit for taxpayers, and rightly so. The money will be used to reduce the national debt by over half a billion pounds.

“This is another step in the long journey in putting right what went so badly wrong in the British economy; it’s another step in repairing the banks; it’s another step in getting the money back for the taxpayer; and it’s another step in reducing our national debt.

“All of those things together are good news.

“If you look at what has happened over the last 12 hours with Lloyds, you have investors from around the world investing in a British bank. That is a sign the British economy is turning a corner.”

Treasury Chief Secretary Danny Alexander told BBC Radio 5 Live: “The Chancellor and I had advice yesterday from Treasury officials and UKFI that this was the right time to start the process of selling. We have sold a smallish chunk of our shareholding in Lloyds, we have sold it at a price that is above the price that the previous government paid for it.

“I think that what it shows is that our economy is turning a corner, that we are now in a position where overseas investors and others are looking to invest in British banks. Given the massive commitment that the British taxpayer made to rescuing these banks when things went wrong back at the time of the financial crisis, I think that it is a welcome sign that we are starting the process, and of course it will be a long process, of getting the taxpayers’ money back.”

He added: “This is the first stage of a very long process. Of course we have major stakes still in Lloyds Banking Group and, of course this will take much longer, in the Royal Bank of Scotland. But what we have done through this transaction is recover the money that the taxpayer put in and in addition made a contribution to paying down the national debt. That must be the right thing to do.”