By Emma Rumney LONDON, Oct 29 (Reuters) - The British government has set out its exit strategy from its biggest taxpayer-funded bailout of the financial crisis, announcing plans to sell all of its shares in Royal Bank of Scotland by 2024. The government owns 62.4 percent of RBS, Britain's fourth-biggest bank by market value, which it rescued in 2008 with a 45.5 billion pound capital injection. The Office for Budget Responsibility, Britain's budget watchdog, said in a document published on Monday that the government planned no further sales this year but would raise 20.6 billion pounds ($26.4 billion) by selling its remaining shares over the next five years. "We consider it reasonable this plan can be achieved," the document said, adding that RBS had made good progress in turning itself around and drawing a line under crisis-era legal problems.