Britain's state-rescued lender Lloyds Banking Group said it has increased the amount of TSB shares it is selling due to keen investor demand.

Shares in TSB rose sharply after its debut on the London Stock Exchange after Lloyds Banking Group sold more of the offshoot business than originally planned, raising the prospect of a further sale this year.

Lloyds said today it had sold a 35% stake in TSB, Britain's 7th-largest lender, at 260 pence a share. That valued the business at £1.3 billion, less than the figure on Lloyds' books.

The TSB share sale is another step on the recovery path for Lloyds following its £20 billion state bailout in 2008 and will help clear the way for the government to sell its remaining 25% Lloyds stake.

TSB shares hit a high of 299.75 pence today, up 15% on the initial public offering (IPO) price. That pushed the bank's market value up to £1.5 billion, or 0.95 times book value.

"Success here is helpful to Lloyds with a potential follow-on rally in the TSB shares encouraging the market to think about an exit closer to book value than had been feared," said Deutsche Bank analyst Jason Napier.

Lloyds had announced its intention to float part of TSB last month, in an effort to meet European Union competition rules over its 2008 government bailout.

The group had originally planned to sell 25% of TSB, or 125 million shares, with a price range between 220 pence and 260 pence per share.

"The successful initial public offering of TSB is an important further step for Lloyds Banking Group as we act to meet our commitments to the European Commission," the bank's chief executive Antonio Horta-Osorio said in today's statement. 

"The significant investor demand for shares in TSB, which reflects investors' confidence in the prospects for the business, has meant that we have been able to set the offer size at 35%. TSB has a national network of branches, a strong capital base, robust liquidity and significant economic protection against legacy issues," he added.

The part-nationalised Lloyds Banking Group relaunched TSB as a standalone lender last September as it prepares for LBG's full return to the private sector. 

The lender plans to complete a full sale of TSB by the end of 2015.