* Graphic: World FX rates in 2020 tmsnrt.rs/2RBWI5E * London, Brussels agree to go "extra mile" * Analysts warn that pound"s gains may not last * U.S. policymakers seen increasing bond purchases this week By Stanley White and Kevin Buckland TOKYO, Dec 14 (Reuters) - The British pound rose against the dollar and euro on hopes that Britain and the European Union will secure a free trade agreement after their decision to extend negotiations beyond the Sunday deadline. The dollar traded near a 2 1/2-year low against major peers ahead of a U.S. Federal Reserve meeting ending Wednesday where policymakers are expected to increase purchases of longer-dated Treasuries to contain a rise in yields. The rally in sterling may not last, some analysts warn, because Britain and the EU have repeatedly struggled to narrow their differences and there is still a risk that trade and business will be thrown into chaos without an agreement. "This is a temporary move higher in the pound, but it is still not clear that a no-deal scenario can be avoided," said Junichi Ishikawa, senior foreign exchange strategist at IG Securities in Tokyo. "A partial deal with an agreement to negotiate further next year might save the pound, but anything less would lead to renewed selling. I would not buy sterling from here." The British pound jumped by 0.72% to $1.3311, its biggest one-day gain since Dec. 1. Against the euro, sterling rose by 0.53% to 91.10 pence. The euro edged up 0.21% to $1.2133. The dollar was little changed at 104.04 yen. London and Brussels agreed on Sunday to "go the extra mile" in coming days to try to reach a trade agreement despite missing their latest deadline to avert a turbulent exit for Britain from the European Union at the end of the month. Britain formally left the EU in January, but has since been in a transition period during which it remains in the EU single market and customs union, meaning that rules on trade, travel and business have stayed the same. That all ends on Dec. 31, and if by then there is no agreement to protect around $1 trillion in annual trade from tariffs and quotas, businesses on both sides would be hit hard, but the British pound is more vulnerable to selling than the euro, analysts warn. The dollar, which has also been under selling pressure recently, faces a big week because of the Fed"s policy meeting. U.S. dollar net short positioning in the latest week climbed to its highest since late September, according to calculations by Reuters and Commodity Futures Trading Commission data released on Friday. The dollar index against a basket of six major currencies stood at 90.775, close to a 2 1/2-year low. Investors have sold the dollar on expectations of a global recovery, buoyed by positive coronavirus vaccine news and hopes for further U.S. stimulus that should lift the market"s risk appetite. The first shipments of coronavirus vaccines have begun spreading across the United States. In addition, there is hope for more fiscal stimulus after Reuters reported the $908 billion relief plan will be split in two in an effort to win approval and could be introduced as early as Monday. The dollar is also under pressure due to expectations that U.S. interest rates will remain low for an extended period. "The secular trend remains overwhelmingly of U.S. dollar weakness," Tapas Strickland, a director of economics at National Australia Bank in Sydney, wrote in a research note. Elsewhere, the onshore yuan edged up to 6.5384 as traders shrugged off steps taken by the People"s Bank of China to slow capital inflows and ease upward pressure on its currency. The Australian dollar was little changed at $0.7540. Central bank minutes on Tuesday could prompt investors to scale back bets for additional monetary easing. Across the Tasman Sea, the New Zealand dollar held steady ahead of data later in the week forecast to show a sharp rebound in the country"s gross domestic product. ======================================================== Currency bid prices at 2:35PM (0535 GMT) Description RIC Last U.S. Close Pct Change YTD Pct High Bid Low Bid Previous Change Session Euro/Dollar $1.2133 $1.2108 +0.21% +8.23% +1.2143 +1.2110 Dollar/Yen 104.0400 104.0150 +0.03% -4.20% +104.0550 +103.8950 Euro/Yen 126.22 125.96 +0.21% +3.50% +126.3400 +125.9900 Dollar/Swiss 0.8891 0.8898 -0.07% -8.11% +0.8895 +0.8885 Sterling/Dollar 1.3311 1.3222 +0.72% +0.41% +1.3379 +1.3270 Dollar/Canadian 1.2756 1.2766 -0.06% -1.79% +1.2763 +1.2746 Aussie/Dollar 0.7540 0.7535 +0.07% +7.46% +0.7559 +0.7524 NZ 0.7085 0.7085 +0.03% +5.32% +0.7102 +0.7080 Dollar/Dollar All spots Tokyo spots Europe spots Volatilities Tokyo Forex market info from BOJ (Reporting by Stanley White; Editing by Richard Pullin and Stephen Coates)