Lloyds Banking Group plans to float TSB in June
Lloyds Bank plans to float 25% of its revived TSB business at the end of June with at least some of the shares being made available to the public, it has said.
It comes as the bank reported a 22% rise in underlying first quarter pre-tax profit to £1.8bn.
The bank must sell the business, which has been valued by City analysts at around £1.5bn.
It follows the bank's £20.5bn taxpayer-backed rescue in 2008.
The stock market float of TSB is a condition of the Lloyds' bailout, which ultimately required approval from the European Commission (EC).
The EC raised concerns about the size of market share the bank had following the bailout and told Lloyds it must sell off some assets.
Those assets included 632 branches, which the bank initially intended to sell to the Co-op Group's banking arm.
But when that deal collapsed last year Lloyds opted to hive off the branches and revive TSB as a separate brand, 18 years after the two banks merged.
Lloyds added it was making "good progress" in reducing its costs which fell by a further 5% to £2.3bn.
Impairment charges at the bank also fell 57% from a year earlier to £431m.
For the first time in at least two years the bank made no provision for the mis-selling of Payment Protection Insurance (PP).
Lloyds, which is 25% taxpayer-owned, said it also expected to apply in the second half of the year for permission to restart dividend payments to existing shareholders.
Lloyds chief executive António Horta-Osório said the bank had made "good progress" in its first quarter.
"We are supporting and benefitting from the UK economic recovery and are delivering better underlying profitability as well as improved returns for shareholders, from a stronger, lower risk balance sheet," he said.
"And it was this strong performance which enabled the government to further reduce its stake, returning an additional £4.2bn of taxpayers' money in the first quarter."
The government has so far sold two tranches of shares in Lloyds, reducing its stake in the bank from 39% last year to 25% in March.
The first share sale, which saw the government sell a 6% stake to institutional investors, raised £3.2bn. The second sale in March, of a further 8% stake, raised £4.2bn.
Lloyds' statutory pre-tax profit for the first quarter fell 33% to £1.37bn from £2.04bn a year earlier.
But the figure was higher than some analysts expected thanks to a £394m gain from the sale of Lloyds' 21% stake wealth manager St James's Place at the end of last year.
The bank said 2013's statory pre-tax profits were boosted by gains made from the sale of government bonds, which amounted to £776m.
Shares in the bank rose 3.11% to 77.69p, which is still well above the Treasury's break even price of 61.2p per share that it said was needed to recoup the taxpayer's money. That break even price was achieved last year with the share price having risen 10% since then.