* OFT approves plans for Lloyds, RBS branch sales
* OFT forces Lloyds to strengthen TSB prior to sale
* Decision removes barrier to Lloyds share sale - sources
* UK will ask EU for extension to branch sale deadline
* Backing clears way for RBS to sell 315 branches
By Matt Scuffham
LONDON, Sept 11 (Reuters) - Britain's competition regulator has approved plans by Lloyds Banking Group to sell 631 branches, potentially clearing the way for the government to start selling its shares in the bank this week.
Lloyds must sell the branches, which it has re-branded TSB, as a penalty for receiving a 20.5 billion pound ($32.4 billion) bailout during the 2008 financial crisis, which left Britain holding a 39 percent stake.
The Office of Fair Trading (OFT) said on Wednesday it was happy with Lloyds' plans, provided it strengthens TSB's balance sheet prior to a sale of the business next year.
The OFT's backing will remove uncertainty and help clear the way for the government to start selling its shares in the bank, sources with knowledge of government thinking said on Wednesday.
Lloyds said it would make changes to enhance TSB's profitability by over 200 million pounds ($316.27 million) in its first four years. It will also hand TSB 40 million pounds to help it attract customers and develop its branches.
The government is keen for challengers to emerge to break the dominance of its biggest four lenders which control about three-quarters of retail accounts.
"This government is getting on with the biggest overhaul of our banking system for a generation, and more competition is a key part of our vision for the future," UK Finance Minister George Osborne said in a statement.
Shares in Lloyds hit a 3-year high on Tuesday as expectations mounted the British government could start selling its shares this month.
Sources have said it is considering selling around a quarter of its 39 percent stake - worth about 5 billion pounds.
The OFT also said on Wednesday that plans by RBS to sell 315 branches would result in a credible lender to small businesses with sales of between 1 million and 25 million pounds. The OFT expects the business will have the ability to compete and grow over time and has not recommended any changes to the plan.
RBS is selling the branches, codenamed "Rainbow", as a penalty for its 45.5 billion pound bailout during the crisis, which left Britain with an 81 percent shareholding.
OFT backing will enable RBS to proceed with its sale plan. Sources familiar with the sale process said it has a shortlist of three bidders, with separate consortia led by private equity firms Blackstone and Corsair the favorites.
"We are confident that the Rainbow bank will increase competition and choice for households and small businesses in Britain. There is strong interest in the business and we are making good progress with the sale process," RBS said.
Both Lloyds and RBS have experienced difficulties selling the branches with planned sales to the Co-operative Bank and Santander collapsing.
Britain's finance ministry said it would now ask the European Commission to extend a deadline of November this year for Lloyds to sell the branches.
The OFT said it was still concerned about the high market share for Britain's big four banks, and said the disposals will only have a limited impact on market shares for Lloyds and RBS.
Lloyds' market share of the personal current account market will dip to 26 percent from 30 percent.
The OFT plans to complete a more thorough review of competition for SME lending in early 2014.