LONDON (Reuters) - Britain has sold another 500 million pounds ($779 million) worth of shares in Lloyds Banking Group (>> Lloyds Banking Group PLC) and has now raised more than 10 billion pounds through the sale of more than half its stake in the bailed-out bank.

The Treasury said on Tuesday that it had reduced its stake by a further 1 percentage point to 19.93 percent, days after a surprise election triumph for the Conservatives sent the bank's shares soaring to multi-year highs.

Lloyds was rescued during the 2007-9 financial crisis at a cost of 20 billion pounds to taxpayers, leaving Britain with a 41 percent stake.

UK Financial Investments (UKFI), which manages the shareholding, began selling Lloyds shares to institutional investors such as pension funds and insurers in September 2013.

Finance Minister George Osborne has said the government plans to sell at least another 9 billion pounds worth of the shares over the next year, including a sale at a discount to private retail investors.

"These sales have only been made possible by our long term economic plan, and we are determined to build on this success, and to continue to return Lloyds to the private sector and reduce our national debt," Osborne said on Tuesday.

The latest sale was through a "pre-arranged trading plan", which UKFI appointed U.S. investment bank Morgan Stanley to undertake. The government's stake has been cut from 24.9 percent through the plan, which was launched last December, raising over 2.5 billion pounds for taxpayers.

Britain's remaining stake in Lloyds is valued at about 12 billion pounds, based on current share prices.

Osborne is expected to press ahead with a plan to sell Lloyds shares to private investors later this year and the government could sell around 4 billion pounds worth of stock through a retail offer, sources said.

The government has said the retail offer would be sold at a 5 percent discount to market value. Investors would be able to buy between 250 pounds and 10,000 pounds worth of Lloyds shares, with priority going to orders of up to 1,000 pounds.

The government is also considering a sale of its shares in Royal Bank of Scotland (>> Royal Bank of Scotland Group plc) later this year and could begin selling the shares at a loss, sources told Reuters last week.

It is currently sitting on a loss of more than 13 billion pounds on its RBS investment.

(Reporting by Matt Scuffham; Editing by Keith Weir)

By Matt Scuffham